From 3e7cf35b2d0c0bf2ed220684c41dd8a2943e1944 Mon Sep 17 00:00:00 2001
From: Richard Milewski <richard+github@milewski.org>
Date: Wed, 28 Jan 2026 13:26:50 -0800
Subject: [PATCH 01/16] Trig fix 1

---
 trigonometry.scad | 21 +++++++++++++++++----
 1 file changed, 17 insertions(+), 4 deletions(-)

diff --git a/trigonometry.scad b/trigonometry.scad
index 8aa49c5..22b2ebe 100644
--- a/trigonometry.scad
+++ b/trigonometry.scad
@@ -120,13 +120,11 @@ function law_of_sines(a, A, b, B) =
 
 
 // Function: hyp_opp_to_adj()
-// Alias: opp_hyp_to_adj()
 // Synopsis: Returns the adjacent side length from the lengths of the hypotenuse and the opposite side.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: opp_hyp_to_adj(), adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
 // Usage:
 //   adj = hyp_opp_to_adj(hyp,opp);
-//   adj = opp_hyp_to_adj(opp,hyp);
 // Description:
 //   Given the lengths of the hypotenuse and opposite side of a right triangle, returns the length
 //   of the adjacent side.
@@ -134,12 +132,27 @@ function law_of_sines(a, A, b, B) =
 //   hyp = The length of the hypotenuse of the right triangle.
 //   opp = The length of the side of the right triangle that is opposite from the primary angle.
 // Example:
-//   hyp = hyp_opp_to_adj(5,3);  // Returns: 4
+//   adj = hyp_opp_to_adj(5,3);  // Returns: 4
 function hyp_opp_to_adj(hyp,opp) =
     assert(is_finite(hyp+opp) && hyp>=0 && opp>=0,
            "Triangle side lengths should be a positive numbers." )
     sqrt(hyp*hyp-opp*opp);
 
+
+// Function: opp_hyp_to_adj()
+// Synopsis: Returns the adjacent side length from the lengths of the hypotenuse and the opposite side.
+// Topics: Geometry, Trigonometry, Triangles
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// Usage:
+//   adj = opp_hyp_to_adj(opp,hyp);
+// Description:
+//   Given the lengths of the opposite side and hypotenuse of a right triangle, returns the length
+//   of the adjacent side.
+// Arguments:
+//   opp = The length of the side of the right triangle that is opposite from the primary angle.
+//   hyp = The length of the hypotenuse of the right triangle.
+// Example:
+//   adj = opp_hyp_to_adj(3,5);  // Returns: 4
 function opp_hyp_to_adj(opp,hyp) = hyp_opp_to_adj(hyp,opp);
 
 

From 0de3e855757950340827cdafd26f6aeb5961353f Mon Sep 17 00:00:00 2001
From: Richard Milewski <richard+github@milewski.org>
Date: Wed, 28 Jan 2026 13:40:50 -0800
Subject: [PATCH 02/16] Trig fix 2

---
 trigonometry.scad | 18 +++++++++++++++---
 1 file changed, 15 insertions(+), 3 deletions(-)

diff --git a/trigonometry.scad b/trigonometry.scad
index 22b2ebe..c3540fa 100644
--- a/trigonometry.scad
+++ b/trigonometry.scad
@@ -142,7 +142,7 @@ function hyp_opp_to_adj(hyp,opp) =
 // Function: opp_hyp_to_adj()
 // Synopsis: Returns the adjacent side length from the lengths of the hypotenuse and the opposite side.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: hyp_opp_to_adj(), adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
 // Usage:
 //   adj = opp_hyp_to_adj(opp,hyp);
 // Description:
@@ -157,13 +157,11 @@ function opp_hyp_to_adj(opp,hyp) = hyp_opp_to_adj(hyp,opp);
 
 
 // Function: hyp_ang_to_adj()
-// Alias: ang_hyp_to_adj()
 // Synopsis: Returns the adjacent side length from the length of the hypotenuse and the angle.
 // Topics: Geometry, Trigonometry, Triangles
 // See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
 // Usage:
 //   adj = hyp_ang_to_adj(hyp,ang);
-//   adj = ang_hyp_to_adj(ang,hyp);
 // Description:
 //   Given the length of the hypotenuse and the angle of the primary corner of a right triangle,
 //   returns the length of the adjacent side.
@@ -177,6 +175,20 @@ function hyp_ang_to_adj(hyp,ang) =
     assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
     hyp*cos(ang);
 
+// Function: ang_hyp_to_adj()
+// Synopsis: Returns the adjacent side length from the angle and the length of the hypotenuse.
+// Topics: Geometry, Trigonometry, Triangles
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// Usage:
+//   adj = ang_hyp_to_adj(ang,hyp);
+// Description:
+//   Given  the angle of the primary corner and the length of the hypotenuse of a right triangle,
+//   returns the length of the adjacent side.
+// Arguments:
+//   ang = The angle in degrees of the primary corner of the right triangle.
+//   hyp = The length of the hypotenuse of the right triangle.
+// Example:
+//   adj = ang_hyp_to_adj(60,8);  // Returns: 4
 function ang_hyp_to_adj(ang,hyp) = hyp_ang_to_adj(hyp, ang);
 
 

From bb5ded67c814b38e20109d9d698c2e8715630dd6 Mon Sep 17 00:00:00 2001
From: Richard Milewski <richard+github@milewski.org>
Date: Wed, 28 Jan 2026 13:49:54 -0800
Subject: [PATCH 03/16] Trig fix 3

---
 trigonometry.scad | 21 ++++++++++++++++++---
 1 file changed, 18 insertions(+), 3 deletions(-)

diff --git a/trigonometry.scad b/trigonometry.scad
index c3540fa..3f8c851 100644
--- a/trigonometry.scad
+++ b/trigonometry.scad
@@ -217,15 +217,13 @@ function ang_opp_to_adj(ang,opp) = opp_ang_to_adj(opp,ang);
 
 
 // Function: hyp_adj_to_opp()
-// Alias: adj_hyp_to_opp()
 // Synopsis: Returns the opposite side length from the lengths of the hypotenuse and the adjacent side.
 // Topics: Geometry, Trigonometry, Triangles
 // See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
 // Usage:
 //   opp = hyp_adj_to_opp(hyp,adj);
-//   opp = adj_hyp_to_opp(adj,hyp);
 // Description:
-//   Given the length of the hypotenuse and the adjacent side, returns the length of the opposite side.
+//   Given the lengths of the hypotenuse and the adjacent side, returns the length of the opposite side.
 // Arguments:
 //   hyp = The length of the hypotenuse of the right triangle.
 //   adj = The length of the side of the right triangle that is adjacent to the primary angle.
@@ -236,9 +234,26 @@ function hyp_adj_to_opp(hyp,adj) =
            "Triangle side lengths should be a positive numbers." )
     sqrt(hyp*hyp-adj*adj);
 
+
+
+// Function: adj_hyp_to_opp()
+// Synopsis: Returns the opposite side length from the lengths of the adjacent side and the hypotenuse.
+// Topics: Geometry, Trigonometry, Triangles
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// Usage:
+//   opp = adj_hyp_to_opp(adj,hyp);
+// Description:
+//   Given the lengths of the adjacent side and the hypotenuse, returns the length of the opposite side.
+// Arguments:
+//   adj = The length of the side of the right triangle that is adjacent to the primary angle.
+//   hyp = The length of the hypotenuse of the right triangle.
+// Example:
+//   opp = adj_hyp_to_opp(4,5);  // Returns: 3
+
 function adj_hyp_to_opp(adj,hyp) = hyp_adj_to_opp(hyp,adj);
 
 
+
 // Function: hyp_ang_to_opp()
 // Alias: ang_hyp_to_opp()
 // Synopsis: Returns the opposite side length from the length of the hypotenuse and the angle.

From 7db0b2b54215a41a1861e17b4e955cc6972d1b6d Mon Sep 17 00:00:00 2001
From: Richard Milewski <richard+github@milewski.org>
Date: Wed, 28 Jan 2026 14:07:14 -0800
Subject: [PATCH 04/16] Trig fix 5

---
 trigonometry.scad | 20 ++++++++++++++++----
 1 file changed, 16 insertions(+), 4 deletions(-)

diff --git a/trigonometry.scad b/trigonometry.scad
index 3f8c851..a76e604 100644
--- a/trigonometry.scad
+++ b/trigonometry.scad
@@ -255,15 +255,13 @@ function adj_hyp_to_opp(adj,hyp) = hyp_adj_to_opp(hyp,adj);
 
 
 // Function: hyp_ang_to_opp()
-// Alias: ang_hyp_to_opp()
-// Synopsis: Returns the opposite side length from the length of the hypotenuse and the angle.
+// Synopsis: Returns the opposite side length from the length of the hypotenuse and the primary angle.
 // Topics: Geometry, Trigonometry, Triangles
 // See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
 // Usage:
 //   opp = hyp_ang_to_opp(hyp,ang);
-//   opp = ang_hyp_to_opp(ang,hyp);
 // Description:
-//   Given the length of the hypotenuse of a right triangle, and the angle of the corner, returns the length of the opposite side.
+//   Given the length of the hypotenuse of a right triangle and the angle of the primary corner, returns the length of the opposite side.
 // Arguments:
 //   hyp = The length of the hypotenuse of the right triangle.
 //   ang = The angle in degrees of the primary corner of the right triangle.
@@ -274,6 +272,20 @@ function hyp_ang_to_opp(hyp,ang) =
     assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
     hyp*sin(ang);
 
+
+// Function: ang_hyp_to_opp()
+// Synopsis: Returns the opposite side length from the primary angle and the length of the hypotenuse.
+// Topics: Geometry, Trigonometry, Triangles
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// Usage:
+//   opp = ang_hyp_to_opp(ang,hyp);
+// Description:
+//   Given the the angle of the primary corner and the length of the hypotenuse of a right triangle, returns the length of the opposite side.
+// Arguments:
+//   ang = The angle in degrees of the primary corner of the right triangle.
+//   hyp = The length of the hypotenuse of the right triangle.
+// Example:
+//   opp = ang_hyp_to_opp(30,8);  // Returns: 4
 function ang_hyp_to_opp(ang,hyp) = hyp_ang_to_opp(hyp,ang);
 
 

From 0d2118b8a2ac932b4acd26c021e66da89c08382b Mon Sep 17 00:00:00 2001
From: Richard Milewski <richard+github@milewski.org>
Date: Wed, 28 Jan 2026 14:40:24 -0800
Subject: [PATCH 05/16] Trig fix

---
 trigonometry.scad | 21 +++++++++++++++++----
 1 file changed, 17 insertions(+), 4 deletions(-)

diff --git a/trigonometry.scad b/trigonometry.scad
index a76e604..352f027 100644
--- a/trigonometry.scad
+++ b/trigonometry.scad
@@ -193,15 +193,13 @@ function ang_hyp_to_adj(ang,hyp) = hyp_ang_to_adj(hyp, ang);
 
 
 // Function: opp_ang_to_adj()
-// Alias: ang_opp_to_adj()
-// Synopsis: Returns the adjacent side length from the length of the opposite side and the angle.
+// Synopsis: Returns the adjacent side length from the length of the opposite side and the primary angle.
 // Topics: Geometry, Trigonometry, Triangles
 // See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
 // Usage:
 //   adj = opp_ang_to_adj(opp,ang);
-//   adj = ang_opp_to_adj(ang,opp);
 // Description:
-//   Given the angle of the primary corner of a right triangle, and the length of the side opposite of it,
+//   Given the length of the side opposite the primary corner, and the angle of the primary corner of a right triangle,
 //   returns the length of the adjacent side.
 // Arguments:
 //   opp = The length of the side of the right triangle that is opposite from the primary angle.
@@ -212,7 +210,22 @@ function opp_ang_to_adj(opp,ang) =
     assert(is_finite(opp) && opp>=0, "Triangle side length should be a positive number." )
     assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
     opp/tan(ang);
+function ang_opp_to_adj(ang,opp) = opp_ang_to_adj(opp,ang);
 
+// Function: ang_opp_to_adj()
+// Synopsis: Returns the adjacent side length from the primary angle and the length of the opposite side.
+// Topics: Geometry, Trigonometry, Triangles
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// Usage:
+//   adj = ang_opp_to_adj(ang,opp);
+// Description:
+//   Given the angle of the primary corner of a right triangle, and the length of the side opposite of it,
+//   returns the length of the adjacent side.
+// Arguments:
+//   ang = The angle in degrees of the primary corner of the right triangle.
+//   opp = The length of the side of the right triangle that is opposite from the primary angle.
+// Example:
+//   adj = ang_opp_to_adj(30,8);  // Returns: 4
 function ang_opp_to_adj(ang,opp) = opp_ang_to_adj(opp,ang);
 
 

From 5af613281a9a921f5faff4a732322f4204e8fde9 Mon Sep 17 00:00:00 2001
From: Richard Milewski <richard+github@milewski.org>
Date: Wed, 28 Jan 2026 14:47:57 -0800
Subject: [PATCH 06/16] Trig Fix

---
 trigonometry.scad | 19 +++++++++++++++----
 1 file changed, 15 insertions(+), 4 deletions(-)

diff --git a/trigonometry.scad b/trigonometry.scad
index 352f027..6483338 100644
--- a/trigonometry.scad
+++ b/trigonometry.scad
@@ -303,15 +303,13 @@ function ang_hyp_to_opp(ang,hyp) = hyp_ang_to_opp(hyp,ang);
 
 
 // Function: adj_ang_to_opp()
-// Alias: ang_adj_to_opp()
-// Synopsis: Returns the opposite side length from the length of the adjacent side and the angle.
+// Synopsis: Returns the opposite side length from the length of the adjacent side and the primary angle.
 // Topics: Geometry, Trigonometry, Triangles
 // See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
 // Usage:
 //   opp = adj_ang_to_opp(adj,ang);
-//   opp = ang_adj_to_opp(ang,adj);
 // Description:
-//   Given the length of the adjacent side of a right triangle, and the angle of the corner, returns the length of the opposite side.
+//   Given the length of the adjacent side of a right triangle, and the angle of the primary corner, returns the length of the opposite side.
 // Arguments:
 //   adj = The length of the side of the right triangle that is adjacent to the primary angle.
 //   ang = The angle in degrees of the primary corner of the right triangle.
@@ -322,6 +320,19 @@ function adj_ang_to_opp(adj,ang) =
     assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
     adj*tan(ang);
 
+// Function: ang_adj_to_opp()
+// Synopsis: Returns the opposite side length from the length of the adjacent side and the primary angle.
+// Topics: Geometry, Trigonometry, Triangles
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// Usage:
+//   opp = ang_adj_to_opp(ang,adj);
+// Description:
+//   Given the angle of the primary corner and the length of the adjacent side of a right triangle, returns the length of the opposite side.
+// Arguments:
+//   ang = The angle in degrees of the primary corner of the right triangle.
+//   adj = The length of the side of the right triangle that is adjacent to the primary angle.
+// Example:
+//   opp = ang_adj_to_opp(45,8);  // Returns: 8
 function ang_adj_to_opp(ang,adj) = adj_ang_to_opp(adj,ang);
 
 

From 1a7029faeba8f101b241eab04d262fd6e9fc4648 Mon Sep 17 00:00:00 2001
From: Richard Milewski <richard+github@milewski.org>
Date: Wed, 28 Jan 2026 14:54:39 -0800
Subject: [PATCH 07/16] Trig Fix

---
 trigonometry.scad | 16 ++++++++++++++--
 1 file changed, 14 insertions(+), 2 deletions(-)

diff --git a/trigonometry.scad b/trigonometry.scad
index 6483338..db2bc81 100644
--- a/trigonometry.scad
+++ b/trigonometry.scad
@@ -337,13 +337,11 @@ function ang_adj_to_opp(ang,adj) = adj_ang_to_opp(adj,ang);
 
 
 // Function: adj_opp_to_hyp()
-// Alias: opp_adj_to_hyp()
 // Synopsis: Returns the hypotenuse length from the lengths of the adjacent and opposite sides.
 // Topics: Geometry, Trigonometry, Triangles
 // See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
 // Usage:
 //   hyp = adj_opp_to_hyp(adj,opp);
-//   hyp = opp_adj_to_hyp(opp,adj);
 // Description:
 //   Given the length of the adjacent and opposite sides of a right triangle, returns the length of the hypotenuse.
 // Arguments:
@@ -356,6 +354,20 @@ function adj_opp_to_hyp(adj,opp) =
            "Triangle side lengths should be a positive numbers." )
     norm([opp,adj]);
 
+
+// Function: opp_adj_to_hyp()
+// Synopsis: Returns the hypotenuse length from the lengths of the opposite and adjacent sides.
+// Topics: Geometry, Trigonometry, Triangles
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// Usage:
+//   hyp = opp_adj_to_hyp(opp,adj);
+// Description:
+//   Given the length of the opposite and adjacent sides of a right triangle, returns the length of the hypotenuse.
+// Arguments:
+//   opp = The length of the side of the right triangle that is opposite from the primary angle.
+//   adj = The length of the side of the right triangle that is adjacent to the primary angle.
+// Example:
+//   hyp = opp_adj_to_hyp(4,3);  // Returns: 5
 function opp_adj_to_hyp(opp,adj) = adj_opp_to_hyp(adj,opp);
 
 

From a8eb06bff32d1b9db69e461f4f9597599be2e28b Mon Sep 17 00:00:00 2001
From: Richard Milewski <richard+github@milewski.org>
Date: Wed, 28 Jan 2026 15:04:05 -0800
Subject: [PATCH 08/16] Trig fix

---
 trigonometry.scad | 18 +++++++++++++++---
 1 file changed, 15 insertions(+), 3 deletions(-)

diff --git a/trigonometry.scad b/trigonometry.scad
index db2bc81..155d964 100644
--- a/trigonometry.scad
+++ b/trigonometry.scad
@@ -372,13 +372,11 @@ function opp_adj_to_hyp(opp,adj) = adj_opp_to_hyp(adj,opp);
 
 
 // Function: adj_ang_to_hyp()
-// Alias: ang_adj_to_hyp()
-// Synopsis: Returns the hypotenuse length from the length of the adjacent and the angle.
+// Synopsis: Returns the hypotenuse length from the length of the adjacent side and the primary angle.
 // Topics: Geometry, Trigonometry, Triangles
 // See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
 // Usage:
 //   hyp = adj_ang_to_hyp(adj,ang);
-//   hyp = ang_adj_to_hyp(ang,adj);
 // Description:
 //   For a right triangle, given the length of the adjacent side, and the corner angle, returns the length of the hypotenuse.
 // Arguments:
@@ -391,6 +389,20 @@ function adj_ang_to_hyp(adj,ang) =
     assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
     adj/cos(ang);
 
+
+// Function: ang_adj_to_hyp()
+// Synopsis: Returns the hypotenuse length from the primary angle and length of the adjacent side.
+// Topics: Geometry, Trigonometry, Triangles
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// Usage:
+//   hyp = ang_adj_to_hyp(ang,adj);
+// Description:
+//   For a right triangle, given the primary angle and length of the adjacent side, returns the length of the hypotenuse.
+// Arguments:
+//   ang = The angle in degrees of the primary corner of the right triangle.
+//   adj = The length of the side of the right triangle that is adjacent to the primary angle.
+// Example:
+//   hyp = ang_adj_to_hyp(60,4);  // Returns: 8
 function ang_adj_to_hyp(ang,adj) = adj_ang_to_hyp(adj,ang);
 
 

From b3d303c1da6e8217dc0f434bead02b25bca66ebe Mon Sep 17 00:00:00 2001
From: Richard Milewski <richard+github@milewski.org>
Date: Wed, 28 Jan 2026 15:32:29 -0800
Subject: [PATCH 09/16] Trig Fix

---
 trigonometry.scad | 38 +++++++++++++++++++++++++++++++-------
 1 file changed, 31 insertions(+), 7 deletions(-)

diff --git a/trigonometry.scad b/trigonometry.scad
index 155d964..66a0caf 100644
--- a/trigonometry.scad
+++ b/trigonometry.scad
@@ -407,15 +407,13 @@ function ang_adj_to_hyp(ang,adj) = adj_ang_to_hyp(adj,ang);
 
 
 // Function: opp_ang_to_hyp()
-// Alias: ang_opp_to_hyp()
-// Synopsis: Returns the hypotenuse length from the length of the opposite side and the angle.
+// Synopsis: Returns the hypotenuse length from the length of the opposite side and the primary angle.
 // Topics: Geometry, Trigonometry, Triangles
 // See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
 // Usage:
 //   hyp = opp_ang_to_hyp(opp,ang);
-//   hyp = ang_opp_to_hyp(ang,opp);
 // Description:
-//   For a right triangle, given the length of the opposite side, and the corner angle, returns the length of the hypotenuse.
+//   For a right triangle, given the length of the opposite side, and the primary corner angle, returns the length of the hypotenuse.
 // Arguments:
 //   opp = The length of the side of the right triangle that is opposite from the primary angle.
 //   ang = The angle in degrees of the primary corner of the right triangle.
@@ -426,19 +424,31 @@ function opp_ang_to_hyp(opp,ang) =
     assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
     opp/sin(ang);
 
+// Function: ang_opp_to_hyp()
+// Synopsis: Returns the hypotenuse length from the primary angle and the length of the opposite side.
+// Topics: Geometry, Trigonometry, Triangles
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// Usage:
+//   hyp = ang_opp_to_hyp(ang,opp);
+// Description:
+//   For a right triangle, given the primary corner angle and the length of the opposite side, returns the length of the hypotenuse.
+// Arguments:
+//   ang = The angle in degrees of the primary corner of the right triangle.
+//   opp = The length of the side of the right triangle that is opposite from the primary angle.
+// Example:
+//   hyp = opp_ang_to_hyp(30,4);  // Returns: 8
 function ang_opp_to_hyp(ang,opp) = opp_ang_to_hyp(opp,ang);
 
 
+
 // Function: hyp_adj_to_ang()
-// Alias: adj_hyp_to_ang()
 // Synopsis: Returns the angle from the lengths of the hypotenuse and the adjacent side.
 // Topics: Geometry, Trigonometry, Triangles
 // See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
 // Usage:
 //   ang = hyp_adj_to_ang(hyp,adj);
-//   ang = adj_hyp_to_ang(adj,hyp);
 // Description:
-//   For a right triangle, given the lengths of the hypotenuse and the adjacent sides, returns the angle of the corner.
+//   For a right triangle, given the lengths of the hypotenuse and the adjacent side, returns the angle of the primary corner.
 // Arguments:
 //   hyp = The length of the hypotenuse of the right triangle.
 //   adj = The length of the side of the right triangle that is adjacent to the primary angle.
@@ -449,6 +459,20 @@ function hyp_adj_to_ang(hyp,adj) =
             "Triangle side lengths should be positive numbers." )
     acos(adj/hyp);
 
+
+// Function: adj_hyp_to_ang()
+// Synopsis: Returns the angle from the lengths of the adjacent side and the hypotenuse.
+// Topics: Geometry, Trigonometry, Triangles
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// Usage:
+//   ang = adj_hyp_to_ang(adj,hyp);
+// Description:
+//   For a right triangle, given the lengths of the adjacent side and the hypotenuse, returns the angle of the primary corner.
+// Arguments:
+//   adj = The length of the side of the right triangle that is adjacent to the primary angle.
+//   hyp = The length of the hypotenuse of the right triangle.
+// Example:
+//   ang = adj_hyp_to_ang(4,8);  // Returns: 60 degrees
 function adj_hyp_to_ang(adj,hyp) = hyp_adj_to_ang(hyp,adj);
 
 

From 6458926c43c3283fd9168ae2f36c7a8e6dd9e9ec Mon Sep 17 00:00:00 2001
From: Richard Milewski <richard+github@milewski.org>
Date: Wed, 28 Jan 2026 15:44:10 -0800
Subject: [PATCH 10/16] Update trigonometry.scad

---
 trigonometry.scad | 41 ++++++++++++++++++++++++++++++++++++++---
 1 file changed, 38 insertions(+), 3 deletions(-)

diff --git a/trigonometry.scad b/trigonometry.scad
index 66a0caf..7c05de4 100644
--- a/trigonometry.scad
+++ b/trigonometry.scad
@@ -478,14 +478,13 @@ function adj_hyp_to_ang(adj,hyp) = hyp_adj_to_ang(hyp,adj);
 
 // Function: hyp_opp_to_ang()
 // Alias: opp_hyp_to_ang()
-// Synopsis: Returns the angle from the lengths of the hypotenuse and the opposite side.
+// Synopsis: Returns the primary angle from the lengths of the hypotenuse and the opposite side.
 // Topics: Geometry, Trigonometry, Triangles
 // See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
 // Usage:
 //   ang = hyp_opp_to_ang(hyp,opp);
-//   ang = opp_hyp_to_ang(opp,hyp);
 // Description:
-//   For a right triangle, given the lengths of the hypotenuse and the opposite sides, returns the angle of the corner.
+//   For a right triangle, given the lengths of the hypotenuse and the opposite sides, returns the angle of the primary corner.
 // Arguments:
 //   hyp = The length of the hypotenuse of the right triangle.
 //   opp = The length of the side of the right triangle that is opposite from the primary angle.
@@ -496,9 +495,45 @@ function hyp_opp_to_ang(hyp,opp) =
             "Triangle side lengths should be positive numbers." )
     asin(opp/hyp);
 
+/ Function: opp_hyp_to_ang()
+// Synopsis: Returns the primary angle from the lengths of the opposite side and the hypotenuse.
+// Topics: Geometry, Trigonometry, Triangles
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// Usage:
+//   ang = opp_hyp_to_ang(opp,hyp);
+// Description:
+//   For a right triangle, given the lengths of the opposite side and the hypotenuse, returns the angle of the primary corner.
+// Arguments:
+//   opp = The length of the side of the right triangle that is opposite from the primary angle.
+//   hyp = The length of the hypotenuse of the right triangle.
+// Example:
+//   ang = opp_hyp_to_ang(4,8);  // Returns: 30 degrees
 function opp_hyp_to_ang(opp,hyp) = hyp_opp_to_ang(hyp,opp);
 
 
+// Function: hyp_adj_to_ang()
+// Alias: adj_hyp_to_ang()
+// Synopsis: Returns the angle from the lengths of the hypotenuse and the adjacent side.
+// Topics: Geometry, Trigonometry, Triangles
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// Usage:
+//   ang = hyp_adj_to_ang(hyp,adj);
+//   ang = adj_hyp_to_ang(adj,hyp);
+// Description:
+//   For a right triangle, given the lengths of the hypotenuse and the adjacent sides, returns the angle of the corner.
+// Arguments:
+//   hyp = The length of the hypotenuse of the right triangle.
+//   adj = The length of the side of the right triangle that is adjacent to the primary angle.
+// Example:
+//   ang = hyp_adj_to_ang(8,4);  // Returns: 60 degrees
+function hyp_adj_to_ang(hyp,adj) =
+    assert(is_finite(hyp) && hyp>0 && is_finite(adj) && adj>=0,
+            "Triangle side lengths should be positive numbers." )
+    acos(adj/hyp);
+
+function adj_hyp_to_ang(adj,hyp) = hyp_adj_to_ang(hyp,adj);
+
+
 // Function: adj_opp_to_ang()
 // Alias: opp_adj_to_ang()
 // Synopsis: Returns the angle from the lengths of the adjacent and opposite sides.

From 56cc15f8abb8ae8fe58972d464eab0c67b7e7734 Mon Sep 17 00:00:00 2001
From: Richard Milewski <richard+github@milewski.org>
Date: Wed, 28 Jan 2026 15:51:45 -0800
Subject: [PATCH 11/16] Update trigonometry.scad

---
 trigonometry.scad | 20 ++++++++++++++++----
 1 file changed, 16 insertions(+), 4 deletions(-)

diff --git a/trigonometry.scad b/trigonometry.scad
index 7c05de4..e3b8905 100644
--- a/trigonometry.scad
+++ b/trigonometry.scad
@@ -495,7 +495,7 @@ function hyp_opp_to_ang(hyp,opp) =
             "Triangle side lengths should be positive numbers." )
     asin(opp/hyp);
 
-/ Function: opp_hyp_to_ang()
+// Function: opp_hyp_to_ang()
 // Synopsis: Returns the primary angle from the lengths of the opposite side and the hypotenuse.
 // Topics: Geometry, Trigonometry, Triangles
 // See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
@@ -512,15 +512,13 @@ function opp_hyp_to_ang(opp,hyp) = hyp_opp_to_ang(hyp,opp);
 
 
 // Function: hyp_adj_to_ang()
-// Alias: adj_hyp_to_ang()
 // Synopsis: Returns the angle from the lengths of the hypotenuse and the adjacent side.
 // Topics: Geometry, Trigonometry, Triangles
 // See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
 // Usage:
 //   ang = hyp_adj_to_ang(hyp,adj);
-//   ang = adj_hyp_to_ang(adj,hyp);
 // Description:
-//   For a right triangle, given the lengths of the hypotenuse and the adjacent sides, returns the angle of the corner.
+//   For a right triangle, given the lengths of the hypotenuse and the adjacent sides, returns the angle of the primary corner.
 // Arguments:
 //   hyp = The length of the hypotenuse of the right triangle.
 //   adj = The length of the side of the right triangle that is adjacent to the primary angle.
@@ -531,6 +529,20 @@ function hyp_adj_to_ang(hyp,adj) =
             "Triangle side lengths should be positive numbers." )
     acos(adj/hyp);
 
+
+// Function: adj_hyp_to_ang()
+// Synopsis: Returns the angle from the lengths of the adjacent side and the hypotenuse.
+// Topics: Geometry, Trigonometry, Triangles
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// Usage:
+//   ang = adj_hyp_to_ang(adj,hyp);
+// Description:
+//   For a right triangle, given the lengths of the adjacent side and the hypotenuse, returns the angle of the primary corner.
+// Arguments:
+//   adj = The length of the side of the right triangle that is adjacent to the primary angle.
+//   hyp = The length of the hypotenuse of the right triangle.
+// Example:
+//   ang = adj_hyp_to_ang(4,8);  // Returns: 60 degrees
 function adj_hyp_to_ang(adj,hyp) = hyp_adj_to_ang(hyp,adj);
 
 

From ddd3245ba01cae68eff0d62c2aa8afc0869f1362 Mon Sep 17 00:00:00 2001
From: Richard Milewski <richard+github@milewski.org>
Date: Wed, 28 Jan 2026 15:57:19 -0800
Subject: [PATCH 12/16] Update trigonometry.scad

---
 trigonometry.scad | 17 +++++++++++++++--
 1 file changed, 15 insertions(+), 2 deletions(-)

diff --git a/trigonometry.scad b/trigonometry.scad
index e3b8905..fe1ac41 100644
--- a/trigonometry.scad
+++ b/trigonometry.scad
@@ -547,13 +547,11 @@ function adj_hyp_to_ang(adj,hyp) = hyp_adj_to_ang(hyp,adj);
 
 
 // Function: adj_opp_to_ang()
-// Alias: opp_adj_to_ang()
 // Synopsis: Returns the angle from the lengths of the adjacent and opposite sides.
 // Topics: Geometry, Trigonometry, Triangles
 // See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
 // Usage:
 //   ang = adj_opp_to_ang(adj,opp);
-//   ang = opp_adj_to_ang(opp,adj);
 // Description:
 //   For a right triangle, given the lengths of the adjacent and opposite sides, returns the angle of the corner.
 // Arguments:
@@ -566,8 +564,23 @@ function adj_opp_to_ang(adj,opp) =
             "Triangle side lengths should be positive numbers." )
     atan2(opp,adj);
 
+
+// Function: opp_adj_to_ang()
+// Synopsis: Returns the primary angle from the lengths of the opposite and adjacent sides.
+// Topics: Geometry, Trigonometry, Triangles
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// Usage:
+//   ang = opp_adj_to_ang(opp,adj);
+// Description:
+//   For a right triangle, given the lengths of the opposite and adjacent sides, returns the angle of the primary corner.
+// Arguments:
+//   opp = The length of the side of the right triangle that is opposite from the primary angle.
+//   adj = The length of the side of the right triangle that is adjacent to the primary angle.
+// Example:
+//   ang = opp_adj_to_ang(0.5,sqrt(3)/2);  // Returns: 30 degrees
 function opp_adj_to_ang(opp,adj) = adj_opp_to_ang(adj,opp);
 
 
 
+
 // vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap

From 51096258be82db0b8f82aeb4114eb6dcfed30bd4 Mon Sep 17 00:00:00 2001
From: Richard Milewski <richard+github@milewski.org>
Date: Wed, 28 Jan 2026 16:22:38 -0800
Subject: [PATCH 13/16] Update trigonometry.scad

---
 trigonometry.scad | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/trigonometry.scad b/trigonometry.scad
index fe1ac41..93b52a6 100644
--- a/trigonometry.scad
+++ b/trigonometry.scad
@@ -210,7 +210,6 @@ function opp_ang_to_adj(opp,ang) =
     assert(is_finite(opp) && opp>=0, "Triangle side length should be a positive number." )
     assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
     opp/tan(ang);
-function ang_opp_to_adj(ang,opp) = opp_ang_to_adj(opp,ang);
 
 // Function: ang_opp_to_adj()
 // Synopsis: Returns the adjacent side length from the primary angle and the length of the opposite side.
@@ -583,4 +582,7 @@ function opp_adj_to_ang(opp,adj) = adj_opp_to_ang(adj,opp);
 
 
 
+
+
+
 // vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap

From cb262643c1a44a8696ea3baaf71015c6333e9ff7 Mon Sep 17 00:00:00 2001
From: Richard Milewski <richard+github@milewski.org>
Date: Wed, 28 Jan 2026 16:42:08 -0800
Subject: [PATCH 14/16] Update trigonometry.scad

---
 trigonometry.scad | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/trigonometry.scad b/trigonometry.scad
index 93b52a6..9236d82 100644
--- a/trigonometry.scad
+++ b/trigonometry.scad
@@ -205,7 +205,7 @@ function ang_hyp_to_adj(ang,hyp) = hyp_ang_to_adj(hyp, ang);
 //   opp = The length of the side of the right triangle that is opposite from the primary angle.
 //   ang = The angle in degrees of the primary corner of the right triangle.
 // Example:
-//   adj = opp_ang_to_adj(8,30);  // Returns: 4
+//   adj = opp_ang_to_adj(8,45);  // Returns: 8
 function opp_ang_to_adj(opp,ang) =
     assert(is_finite(opp) && opp>=0, "Triangle side length should be a positive number." )
     assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." )
@@ -224,7 +224,7 @@ function opp_ang_to_adj(opp,ang) =
 //   ang = The angle in degrees of the primary corner of the right triangle.
 //   opp = The length of the side of the right triangle that is opposite from the primary angle.
 // Example:
-//   adj = ang_opp_to_adj(30,8);  // Returns: 4
+//   adj = ang_opp_to_adj(45,8);  // Returns: 8
 function ang_opp_to_adj(ang,opp) = opp_ang_to_adj(opp,ang);
 
 

From 4fbaf957b0e4b2720cd954aab75f5e648e898186 Mon Sep 17 00:00:00 2001
From: Richard Milewski <richard+github@milewski.org>
Date: Wed, 28 Jan 2026 20:28:41 -0800
Subject: [PATCH 15/16] Update trigonometry.scad

---
 trigonometry.scad | 36 ------------------------------------
 1 file changed, 36 deletions(-)

diff --git a/trigonometry.scad b/trigonometry.scad
index 9236d82..abf001a 100644
--- a/trigonometry.scad
+++ b/trigonometry.scad
@@ -476,7 +476,6 @@ function adj_hyp_to_ang(adj,hyp) = hyp_adj_to_ang(hyp,adj);
 
 
 // Function: hyp_opp_to_ang()
-// Alias: opp_hyp_to_ang()
 // Synopsis: Returns the primary angle from the lengths of the hypotenuse and the opposite side.
 // Topics: Geometry, Trigonometry, Triangles
 // See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
@@ -510,41 +509,6 @@ function hyp_opp_to_ang(hyp,opp) =
 function opp_hyp_to_ang(opp,hyp) = hyp_opp_to_ang(hyp,opp);
 
 
-// Function: hyp_adj_to_ang()
-// Synopsis: Returns the angle from the lengths of the hypotenuse and the adjacent side.
-// Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
-// Usage:
-//   ang = hyp_adj_to_ang(hyp,adj);
-// Description:
-//   For a right triangle, given the lengths of the hypotenuse and the adjacent sides, returns the angle of the primary corner.
-// Arguments:
-//   hyp = The length of the hypotenuse of the right triangle.
-//   adj = The length of the side of the right triangle that is adjacent to the primary angle.
-// Example:
-//   ang = hyp_adj_to_ang(8,4);  // Returns: 60 degrees
-function hyp_adj_to_ang(hyp,adj) =
-    assert(is_finite(hyp) && hyp>0 && is_finite(adj) && adj>=0,
-            "Triangle side lengths should be positive numbers." )
-    acos(adj/hyp);
-
-
-// Function: adj_hyp_to_ang()
-// Synopsis: Returns the angle from the lengths of the adjacent side and the hypotenuse.
-// Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
-// Usage:
-//   ang = adj_hyp_to_ang(adj,hyp);
-// Description:
-//   For a right triangle, given the lengths of the adjacent side and the hypotenuse, returns the angle of the primary corner.
-// Arguments:
-//   adj = The length of the side of the right triangle that is adjacent to the primary angle.
-//   hyp = The length of the hypotenuse of the right triangle.
-// Example:
-//   ang = adj_hyp_to_ang(4,8);  // Returns: 60 degrees
-function adj_hyp_to_ang(adj,hyp) = hyp_adj_to_ang(hyp,adj);
-
-
 // Function: adj_opp_to_ang()
 // Synopsis: Returns the angle from the lengths of the adjacent and opposite sides.
 // Topics: Geometry, Trigonometry, Triangles

From 6c5bf83f67c82e7517dbe8c4d1e4dd040a8a7016 Mon Sep 17 00:00:00 2001
From: Richard Milewski <richard+github@milewski.org>
Date: Thu, 29 Jan 2026 09:14:42 -0800
Subject: [PATCH 16/16] Update trigonometry.scad

Add new entries to See Also lines.
---
 trigonometry.scad | 48 +++++++++++++++++++++++------------------------
 1 file changed, 24 insertions(+), 24 deletions(-)

diff --git a/trigonometry.scad b/trigonometry.scad
index abf001a..35b8df1 100644
--- a/trigonometry.scad
+++ b/trigonometry.scad
@@ -122,7 +122,7 @@ function law_of_sines(a, A, b, B) =
 // Function: hyp_opp_to_adj()
 // Synopsis: Returns the adjacent side length from the lengths of the hypotenuse and the opposite side.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: opp_hyp_to_adj(), adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   adj = hyp_opp_to_adj(hyp,opp);
 // Description:
@@ -142,7 +142,7 @@ function hyp_opp_to_adj(hyp,opp) =
 // Function: opp_hyp_to_adj()
 // Synopsis: Returns the adjacent side length from the lengths of the hypotenuse and the opposite side.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: hyp_opp_to_adj(), adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   adj = opp_hyp_to_adj(opp,hyp);
 // Description:
@@ -159,7 +159,7 @@ function opp_hyp_to_adj(opp,hyp) = hyp_opp_to_adj(hyp,opp);
 // Function: hyp_ang_to_adj()
 // Synopsis: Returns the adjacent side length from the length of the hypotenuse and the angle.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   adj = hyp_ang_to_adj(hyp,ang);
 // Description:
@@ -178,7 +178,7 @@ function hyp_ang_to_adj(hyp,ang) =
 // Function: ang_hyp_to_adj()
 // Synopsis: Returns the adjacent side length from the angle and the length of the hypotenuse.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   adj = ang_hyp_to_adj(ang,hyp);
 // Description:
@@ -195,7 +195,7 @@ function ang_hyp_to_adj(ang,hyp) = hyp_ang_to_adj(hyp, ang);
 // Function: opp_ang_to_adj()
 // Synopsis: Returns the adjacent side length from the length of the opposite side and the primary angle.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   adj = opp_ang_to_adj(opp,ang);
 // Description:
@@ -214,7 +214,7 @@ function opp_ang_to_adj(opp,ang) =
 // Function: ang_opp_to_adj()
 // Synopsis: Returns the adjacent side length from the primary angle and the length of the opposite side.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   adj = ang_opp_to_adj(ang,opp);
 // Description:
@@ -231,7 +231,7 @@ function ang_opp_to_adj(ang,opp) = opp_ang_to_adj(opp,ang);
 // Function: hyp_adj_to_opp()
 // Synopsis: Returns the opposite side length from the lengths of the hypotenuse and the adjacent side.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   opp = hyp_adj_to_opp(hyp,adj);
 // Description:
@@ -251,7 +251,7 @@ function hyp_adj_to_opp(hyp,adj) =
 // Function: adj_hyp_to_opp()
 // Synopsis: Returns the opposite side length from the lengths of the adjacent side and the hypotenuse.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   opp = adj_hyp_to_opp(adj,hyp);
 // Description:
@@ -269,7 +269,7 @@ function adj_hyp_to_opp(adj,hyp) = hyp_adj_to_opp(hyp,adj);
 // Function: hyp_ang_to_opp()
 // Synopsis: Returns the opposite side length from the length of the hypotenuse and the primary angle.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   opp = hyp_ang_to_opp(hyp,ang);
 // Description:
@@ -288,7 +288,7 @@ function hyp_ang_to_opp(hyp,ang) =
 // Function: ang_hyp_to_opp()
 // Synopsis: Returns the opposite side length from the primary angle and the length of the hypotenuse.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   opp = ang_hyp_to_opp(ang,hyp);
 // Description:
@@ -304,7 +304,7 @@ function ang_hyp_to_opp(ang,hyp) = hyp_ang_to_opp(hyp,ang);
 // Function: adj_ang_to_opp()
 // Synopsis: Returns the opposite side length from the length of the adjacent side and the primary angle.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   opp = adj_ang_to_opp(adj,ang);
 // Description:
@@ -322,7 +322,7 @@ function adj_ang_to_opp(adj,ang) =
 // Function: ang_adj_to_opp()
 // Synopsis: Returns the opposite side length from the length of the adjacent side and the primary angle.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   opp = ang_adj_to_opp(ang,adj);
 // Description:
@@ -338,7 +338,7 @@ function ang_adj_to_opp(ang,adj) = adj_ang_to_opp(adj,ang);
 // Function: adj_opp_to_hyp()
 // Synopsis: Returns the hypotenuse length from the lengths of the adjacent and opposite sides.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   hyp = adj_opp_to_hyp(adj,opp);
 // Description:
@@ -357,7 +357,7 @@ function adj_opp_to_hyp(adj,opp) =
 // Function: opp_adj_to_hyp()
 // Synopsis: Returns the hypotenuse length from the lengths of the opposite and adjacent sides.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   hyp = opp_adj_to_hyp(opp,adj);
 // Description:
@@ -373,7 +373,7 @@ function opp_adj_to_hyp(opp,adj) = adj_opp_to_hyp(adj,opp);
 // Function: adj_ang_to_hyp()
 // Synopsis: Returns the hypotenuse length from the length of the adjacent side and the primary angle.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   hyp = adj_ang_to_hyp(adj,ang);
 // Description:
@@ -392,7 +392,7 @@ function adj_ang_to_hyp(adj,ang) =
 // Function: ang_adj_to_hyp()
 // Synopsis: Returns the hypotenuse length from the primary angle and length of the adjacent side.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   hyp = ang_adj_to_hyp(ang,adj);
 // Description:
@@ -408,7 +408,7 @@ function ang_adj_to_hyp(ang,adj) = adj_ang_to_hyp(adj,ang);
 // Function: opp_ang_to_hyp()
 // Synopsis: Returns the hypotenuse length from the length of the opposite side and the primary angle.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   hyp = opp_ang_to_hyp(opp,ang);
 // Description:
@@ -426,7 +426,7 @@ function opp_ang_to_hyp(opp,ang) =
 // Function: ang_opp_to_hyp()
 // Synopsis: Returns the hypotenuse length from the primary angle and the length of the opposite side.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   hyp = ang_opp_to_hyp(ang,opp);
 // Description:
@@ -443,7 +443,7 @@ function ang_opp_to_hyp(ang,opp) = opp_ang_to_hyp(opp,ang);
 // Function: hyp_adj_to_ang()
 // Synopsis: Returns the angle from the lengths of the hypotenuse and the adjacent side.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   ang = hyp_adj_to_ang(hyp,adj);
 // Description:
@@ -462,7 +462,7 @@ function hyp_adj_to_ang(hyp,adj) =
 // Function: adj_hyp_to_ang()
 // Synopsis: Returns the angle from the lengths of the adjacent side and the hypotenuse.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   ang = adj_hyp_to_ang(adj,hyp);
 // Description:
@@ -478,7 +478,7 @@ function adj_hyp_to_ang(adj,hyp) = hyp_adj_to_ang(hyp,adj);
 // Function: hyp_opp_to_ang()
 // Synopsis: Returns the primary angle from the lengths of the hypotenuse and the opposite side.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   ang = hyp_opp_to_ang(hyp,opp);
 // Description:
@@ -496,7 +496,7 @@ function hyp_opp_to_ang(hyp,opp) =
 // Function: opp_hyp_to_ang()
 // Synopsis: Returns the primary angle from the lengths of the opposite side and the hypotenuse.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   ang = opp_hyp_to_ang(opp,hyp);
 // Description:
@@ -512,7 +512,7 @@ function opp_hyp_to_ang(opp,hyp) = hyp_opp_to_ang(hyp,opp);
 // Function: adj_opp_to_ang()
 // Synopsis: Returns the angle from the lengths of the adjacent and opposite sides.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   ang = adj_opp_to_ang(adj,opp);
 // Description:
@@ -531,7 +531,7 @@ function adj_opp_to_ang(adj,opp) =
 // Function: opp_adj_to_ang()
 // Synopsis: Returns the primary angle from the lengths of the opposite and adjacent sides.
 // Topics: Geometry, Trigonometry, Triangles
-// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp()
+// See Also: adj_ang_to_hyp(), adj_ang_to_opp(), adj_opp_to_ang(), adj_opp_to_hyp(), hyp_adj_to_ang(), hyp_adj_to_opp(), hyp_ang_to_adj(), hyp_ang_to_opp(), hyp_opp_to_adj(), hyp_opp_to_ang(), opp_ang_to_adj(), opp_ang_to_hyp(), ang_adj_to_hyp(), ang_adj_to_opp(), opp_adj_to_ang(), opp_adj_to_hyp(), adj_hyp_to_ang(), adj_hyp_to_opp(), ang_hyp_to_adj(), ang_hyp_to_opp(), opp_hyp_to_adj(), opp_hyp_to_ang(), ang_opp_to_adj(), ang_opp_to_hyp()
 // Usage:
 //   ang = opp_adj_to_ang(opp,adj);
 // Description: