From b6dd763e79beabeb2585480701de2fbc092b9a8c Mon Sep 17 00:00:00 2001 From: Richard Milewski Date: Fri, 30 Jan 2026 12:50:54 -0800 Subject: [PATCH] Update trigonometry.scad Fix missed reference angle changes. --- trigonometry.scad | 182 +++++++++++++++++++++++----------------------- 1 file changed, 91 insertions(+), 91 deletions(-) diff --git a/trigonometry.scad b/trigonometry.scad index d8d1d5c..23392cd 100644 --- a/trigonometry.scad +++ b/trigonometry.scad @@ -25,8 +25,8 @@ _BOSL2_TRIGONOMETRY = is_undef(_BOSL2_STD) && (is_undef(BOSL2_NO_STD_WARNING) || // c = law_of_cosines(a, b, C=); // Description: // Applies the Law of Cosines for an arbitrary triangle. Given three side lengths, returns the -// angle in degrees for the corner opposite of the third side. Given two side lengths, and the -// angle between them, returns the length of the third side. +// reference angle in degrees for the corner opposite of the third side. Given two side lengths, and the +// reference angle between them, returns the length of the third side. // Figure(2D;NoAxes;VPD=200;VPT=[0,25,20]): // stroke([[-50,0], [10,60], [50,0]], closed=true, width=2); // color("black") { @@ -44,7 +44,7 @@ _BOSL2_TRIGONOMETRY = is_undef(_BOSL2_STD) && (is_undef(BOSL2_NO_STD_WARNING) || // b = The length of the second side. // c = The length of the third side. // --- -// C = The angle in degrees of the corner opposite of the third side. +// C = The reference angle in degrees of the corner opposite of the third side. function law_of_cosines(a, b, c, C) = // Triangle Law of Cosines: // c^2 = a^2 + b^2 - 2*a*b*cos(C) @@ -62,9 +62,9 @@ function law_of_cosines(a, b, c, C) = // b = law_of_sines(a, A, B=); // Description: // Applies the Law of Sines for an arbitrary triangle. Given two triangle side lengths and the -// angle between them, returns the angle of the corner opposite of the second side. Given a side -// length, the opposing angle, and a second angle, returns the length of the side opposite of the -// second angle. +// reference angle between them, returns the reference angle of the corner opposite of the second side. Given a side +// length, the opposing reference angle, and a second reference angle, returns the length of the side opposite of the +// second reference angle. // Figure(2D;NoAxes;VPD=200;VPT=[0,25,0]): // stroke([[-50,0], [10,60], [50,0]], closed=true, width=2); // color("black") { @@ -79,10 +79,10 @@ function law_of_cosines(a, b, c, C) = // } // Arguments: // a = The length of the first side. -// A = The angle in degrees of the corner opposite of the first side. +// A = The reference angle in degrees of the corner opposite of the first side. // b = The length of the second side. // --- -// B = The angle in degrees of the corner opposite of the second side. +// B = The reference angle in degrees of the corner opposite of the second side. function law_of_sines(a, A, b, B) = // Triangle Law of Sines: // a/sin(A) = b/sin(B) = c/sin(C) @@ -96,15 +96,15 @@ function law_of_sines(a, A, b, B) = // Section: Right Triangle Functions // This is a set of functions to make it easier to perform trig calculations on right triangles. // In general, all these functions are named using these abbreviations: -// - **ang**: The reference angle size in degrees. +// - **ang**: The reference reference angle size in degrees. // - **hyp**: The length of the Hypotenuse. -// - **adj**: The length of the side adjacent to the reference angle. -// - **opp**: The length of the side opposite to the reference angle. +// - **adj**: The length of the side adjacent to the reference reference angle. +// - **opp**: The length of the side opposite to the reference reference angle. // . // If you know two of those, and want to know the value of a third, you will need to call a // function named like `AAA_BBB_to_CCC()`. For example, if you know the length of the hypotenuse, -// and the length of the side adjacent to the reference angle, and want to learn the length of the side -// opposite to the reference angle, you will call `opp = hyp_adj_to_opp(hyp,adj);`. +// and the length of the side adjacent to the reference reference angle, and want to learn the length of the side +// opposite to the reference reference angle, you will call `opp = hyp_adj_to_opp(hyp,adj);`. // Figure(2D;NoAxes;VPD=250:VPT=[10,25,0]): // color("brown") { // stroke([[40,0], [40,10], [50,10]]); @@ -130,7 +130,7 @@ function law_of_sines(a, A, b, B) = // of the adjacent side. // 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 reference angle. +// opp = The length of the side of the right triangle that is opposite from the reference reference angle. // Example: // adj = hyp_opp_to_adj(5,3); // Returns: 4 function hyp_opp_to_adj(hyp,opp) = @@ -149,7 +149,7 @@ function hyp_opp_to_adj(hyp,opp) = // 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 reference angle. +// opp = The length of the side of the right triangle that is opposite from the reference reference angle. // hyp = The length of the hypotenuse of the right triangle. // Example: // adj = opp_hyp_to_adj(3,5); // Returns: 4 @@ -157,35 +157,35 @@ 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. +// Synopsis: Returns the adjacent side length from the length of the hypotenuse and the reference reference 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(), 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: -// Given the length of the hypotenuse and the reference angle of a right triangle, +// Given the length of the hypotenuse and the reference reference angle of a right triangle, // returns the length of the adjacent side. // Arguments: // hyp = The length of the hypotenuse of the right triangle. -// ang = The reference angle of the right triangle in degrees +// ang = The reference reference angle of the right triangle in degrees // Example: // adj = hyp_ang_to_adj(8,60); // Returns: 4 function hyp_ang_to_adj(hyp,ang) = assert(is_finite(hyp) && hyp>=0, "Triangle side length should be a positive number." ) - assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." ) + assert(is_finite(ang) && ang>-90 && ang<90, "The reference angle should be an acute reference angle." ) hyp*cos(ang); // Function: ang_hyp_to_adj() -// Synopsis: Returns the adjacent side length from the angle and the length of the hypotenuse. +// Synopsis: Returns the adjacent side length from the reference reference 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(), 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: -// Given the reference angle and the length of the hypotenuse of a right triangle, +// Given the reference reference angle and the length of the hypotenuse of a right triangle, // returns the length of the adjacent side. // Arguments: -// ang = The reference angle of the right triangle in degrees +// ang = The reference reference angle of the right triangle in degrees // hyp = The length of the hypotenuse of the right triangle. // Example: // adj = ang_hyp_to_adj(60,8); // Returns: 4 @@ -193,36 +193,36 @@ 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 reference angle. +// Synopsis: Returns the adjacent side length from the length of the opposite side and the reference reference 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(), 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: -// Given the length of the opposite side and the reference angle of a right triangle, +// Given the length of the opposite side and the reference reference angle 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 reference angle. -// ang = The reference angle of the right triangle in degrees +// opp = The length of the side of the right triangle that is opposite from the reference reference angle. +// ang = The reference reference angle of the right triangle in degrees // Example: // 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." ) + assert(is_finite(ang) && ang>-90 && ang<90, "The reference angle should be an acute reference angle." ) opp/tan(ang); // Function: ang_opp_to_adj() -// Synopsis: Returns the adjacent side length from the reference angle and the length of the opposite side. +// Synopsis: Returns the adjacent side length from the reference reference 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(), 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: -// Given the reference angle of a right triangle, and the length of the side opposite of it, +// Given the reference reference angle of a right triangle, and the length of the side opposite of it, // returns the length of the adjacent side. // Arguments: -// ang = The reference angle of the right triangle in degrees -// opp = The length of the side of the right triangle that is opposite from the reference angle. +// ang = The reference reference angle of the right triangle in degrees +// opp = The length of the side of the right triangle that is opposite from the reference reference angle. // Example: // adj = ang_opp_to_adj(45,8); // Returns: 8 function ang_opp_to_adj(ang,opp) = opp_ang_to_adj(opp,ang); @@ -238,7 +238,7 @@ function ang_opp_to_adj(ang,opp) = opp_ang_to_adj(opp,ang); // 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 reference angle. +// adj = The length of the side of the right triangle that is adjacent to the reference reference angle. // Example: // opp = hyp_adj_to_opp(5,4); // Returns: 3 function hyp_adj_to_opp(hyp,adj) = @@ -257,7 +257,7 @@ function hyp_adj_to_opp(hyp,adj) = // 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 reference angle. +// adj = The length of the side of the right triangle that is adjacent to the reference reference angle. // hyp = The length of the hypotenuse of the right triangle. // Example: // opp = adj_hyp_to_opp(4,5); // Returns: 3 @@ -267,34 +267,34 @@ 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 reference angle. +// Synopsis: Returns the opposite side length from the length of the hypotenuse and the reference reference 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(), 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: -// Given the length of the hypotenuse of a right triangle and the reference angle, returns the length of the opposite side. +// Given the length of the hypotenuse of a right triangle and the reference reference angle, returns the length of the opposite side. // Arguments: // hyp = The length of the hypotenuse of the right triangle. -// ang = The reference angle of the right triangle in degrees +// ang = The reference reference angle of the right triangle in degrees // Example: // opp = hyp_ang_to_opp(8,30); // Returns: 4 function hyp_ang_to_opp(hyp,ang) = assert(is_finite(hyp)&&hyp>=0, "Triangle side length should be a positive number." ) - assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." ) + assert(is_finite(ang) && ang>-90 && ang<90, "The reference angle should be an acute reference angle." ) hyp*sin(ang); // Function: ang_hyp_to_opp() -// Synopsis: Returns the opposite side length from the reference angle and the length of the hypotenuse. +// Synopsis: Returns the opposite side length from the reference reference 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(), 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: -// Given the the reference angle and the length of the hypotenuse of a right triangle, returns the length of the opposite side. +// Given the the reference reference angle and the length of the hypotenuse of a right triangle, returns the length of the opposite side. // Arguments: -// ang = The reference angle of the right triangle in degrees +// ang = The reference reference angle of the right triangle in degrees // hyp = The length of the hypotenuse of the right triangle. // Example: // opp = ang_hyp_to_opp(30,8); // Returns: 4 @@ -302,34 +302,34 @@ 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 reference angle. +// Synopsis: Returns the opposite side length from the length of the adjacent side and the reference reference 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(), 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: -// Given the length of the adjacent side of a right triangle, and the reference angle, returns the length of the opposite side. +// Given the length of the adjacent side of a right triangle, and the reference reference angle, returns the length of the opposite side. // Arguments: -// adj = The length of the side of the right triangle that is adjacent to the reference angle. -// ang = The reference angle of the right triangle in degrees +// adj = The length of the side of the right triangle that is adjacent to the reference reference angle. +// ang = The reference reference angle of the right triangle in degrees // Example: // opp = adj_ang_to_opp(8,45); // Returns: 8 function adj_ang_to_opp(adj,ang) = assert(is_finite(adj)&&adj>=0, "Triangle side length should be a positive number." ) - assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." ) + assert(is_finite(ang) && ang>-90 && ang<90, "The reference angle should be an acute reference angle." ) adj*tan(ang); // Function: ang_adj_to_opp() -// Synopsis: Returns the opposite side length from the reference angle and the length of the adjacent side. +// Synopsis: Returns the opposite side length from the reference reference angle and the 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(), 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: -// Given the reference angle and the length of the adjacent side of a right triangle, returns the length of the opposite side. +// Given the reference reference angle and the length of the adjacent side of a right triangle, returns the length of the opposite side. // Arguments: -// ang = The reference angle of the right triangle in degrees -// adj = The length of the side of the right triangle that is adjacent to the reference angle. +// ang = The reference reference angle of the right triangle in degrees +// adj = The length of the side of the right triangle that is adjacent to the reference reference angle. // Example: // opp = ang_adj_to_opp(45,8); // Returns: 8 function ang_adj_to_opp(ang,adj) = adj_ang_to_opp(adj,ang); @@ -344,8 +344,8 @@ function ang_adj_to_opp(ang,adj) = adj_ang_to_opp(adj,ang); // Description: // Given the length of the adjacent and opposite sides of a right triangle, returns the length of the hypotenuse. // Arguments: -// adj = The length of the side of the right triangle that is adjacent to the reference angle. -// opp = The length of the side of the right triangle that is opposite from the reference angle. +// adj = The length of the side of the right triangle that is adjacent to the reference reference angle. +// opp = The length of the side of the right triangle that is opposite from the reference reference angle. // Example: // hyp = adj_opp_to_hyp(3,4); // Returns: 5 function adj_opp_to_hyp(adj,opp) = @@ -363,77 +363,77 @@ function adj_opp_to_hyp(adj,opp) = // 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 reference angle. -// adj = The length of the side of the right triangle that is adjacent to the reference angle. +// opp = The length of the side of the right triangle that is opposite from the reference reference angle. +// adj = The length of the side of the right triangle that is adjacent to the reference reference angle. // Example: // hyp = opp_adj_to_hyp(4,3); // Returns: 5 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 reference angle. +// Synopsis: Returns the hypotenuse length from the length of the adjacent side and the reference reference 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(), 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: -// For a right triangle, given the length of the adjacent side, and the corner angle, returns the length of the hypotenuse. +// For a right triangle, given the length of the adjacent side, and the reference reference angle, returns the length of the hypotenuse. // Arguments: -// adj = The length of the side of the right triangle that is adjacent to the reference angle. -// ang = The reference angle of the right triangle in degrees +// adj = The length of the side of the right triangle that is adjacent to the reference reference angle. +// ang = The reference reference angle of the right triangle in degrees // Example: // hyp = adj_ang_to_hyp(4,60); // Returns: 8 function adj_ang_to_hyp(adj,ang) = assert(is_finite(adj) && adj>=0, "Triangle side length should be a positive number." ) - assert(is_finite(ang) && ang>-90 && ang<90, "The angle should be an acute angle." ) + assert(is_finite(ang) && ang>-90 && ang<90, "The reference angle should be an acute reference angle." ) adj/cos(ang); // Function: ang_adj_to_hyp() -// Synopsis: Returns the hypotenuse length from the reference angle and length of the adjacent side. +// Synopsis: Returns the hypotenuse length from the reference reference 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(), 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: -// For a right triangle, given the reference angle and length of the adjacent side, returns the length of the hypotenuse. +// For a right triangle, given the reference reference angle and length of the adjacent side, returns the length of the hypotenuse. // Arguments: -// ang = The reference angle of the right triangle in degrees -// adj = The length of the side of the right triangle that is adjacent to the reference angle. +// ang = The reference reference angle of the right triangle in degrees +// adj = The length of the side of the right triangle that is adjacent to the reference reference angle. // Example: // hyp = ang_adj_to_hyp(60,4); // Returns: 8 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 reference angle. +// Synopsis: Returns the hypotenuse length from the length of the opposite side and the reference reference 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(), 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: -// For a right triangle, given the length of the opposite side, and the reference angle, returns the length of the hypotenuse. +// For a right triangle, given the length of the opposite side, and the reference reference angle, returns the length of the hypotenuse. // Arguments: -// opp = The length of the side of the right triangle that is opposite from the reference angle. -// ang = The reference angle of the right triangle in degrees +// opp = The length of the side of the right triangle that is opposite from the reference reference angle. +// ang = The reference reference angle of the right triangle in degrees // Example: // hyp = opp_ang_to_hyp(4,30); // Returns: 8 function opp_ang_to_hyp(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." ) + assert(is_finite(ang) && ang>-90 && ang<90, "The reference angle should be an acute reference angle." ) opp/sin(ang); // Function: ang_opp_to_hyp() -// Synopsis: Returns the hypotenuse length from the reference angle and the length of the opposite side. +// Synopsis: Returns the hypotenuse length from the reference reference 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(), 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: -// For a right triangle, given the reference angle and the length of the opposite side, returns the length of the hypotenuse. +// For a right triangle, given the reference reference angle and the length of the opposite side, returns the length of the hypotenuse. // Arguments: -// ang = The reference angle of the right triangle in degrees -// opp = The length of the side of the right triangle that is opposite from the reference angle. +// ang = The reference reference angle of the right triangle in degrees +// opp = The length of the side of the right triangle that is opposite from the reference reference angle. // Example: // hyp = opp_ang_to_hyp(30,4); // Returns: 8 function ang_opp_to_hyp(ang,opp) = opp_ang_to_hyp(opp,ang); @@ -441,16 +441,16 @@ 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. +// Synopsis: Returns the reference reference 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(), 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: -// For a right triangle, given the lengths of the hypotenuse and the adjacent side, returns the reference angle. +// For a right triangle, given the lengths of the hypotenuse and the adjacent side, returns the reference reference angle. // 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 reference angle. +// adj = The length of the side of the right triangle that is adjacent to the reference reference angle. // Example: // ang = hyp_adj_to_ang(8,4); // Returns: 60 degrees function hyp_adj_to_ang(hyp,adj) = @@ -460,15 +460,15 @@ 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. +// Synopsis: Returns the reference 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(), 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: -// For a right triangle, given the lengths of the adjacent side and the hypotenuse, returns the reference angle. +// For a right triangle, given the lengths of the adjacent side and the hypotenuse, returns the reference reference angle. // Arguments: -// adj = The length of the side of the right triangle that is adjacent to the reference angle. +// adj = The length of the side of the right triangle that is adjacent to the reference reference angle. // hyp = The length of the hypotenuse of the right triangle. // Example: // ang = adj_hyp_to_ang(4,8); // Returns: 60 degrees @@ -476,16 +476,16 @@ function adj_hyp_to_ang(adj,hyp) = hyp_adj_to_ang(hyp,adj); // Function: hyp_opp_to_ang() -// Synopsis: Returns the reference angle from the lengths of the hypotenuse and the opposite side. +// Synopsis: Returns the reference reference 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(), 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: -// For a right triangle, given the lengths of the hypotenuse and the opposite sides, returns the reference angle. +// For a right triangle, given the lengths of the hypotenuse and the opposite sides, returns the reference reference angle. // 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 reference angle. +// opp = The length of the side of the right triangle that is opposite from the reference reference angle. // Example: // ang = hyp_opp_to_ang(8,4); // Returns: 30 degrees function hyp_opp_to_ang(hyp,opp) = @@ -494,15 +494,15 @@ function hyp_opp_to_ang(hyp,opp) = asin(opp/hyp); // Function: opp_hyp_to_ang() -// Synopsis: Returns the reference angle from the lengths of the opposite side and the hypotenuse. +// Synopsis: Returns the reference reference 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(), 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: -// For a right triangle, given the lengths of the opposite side and the hypotenuse, returns the reference angle. +// For a right triangle, given the lengths of the opposite side and the hypotenuse, returns the reference reference angle. // Arguments: -// opp = The length of the side of the right triangle that is opposite from the reference angle. +// opp = The length of the side of the right triangle that is opposite from the reference reference angle. // hyp = The length of the hypotenuse of the right triangle. // Example: // ang = opp_hyp_to_ang(4,8); // Returns: 30 degrees @@ -510,16 +510,16 @@ 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. +// Synopsis: Returns the reference 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(), 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: -// For a right triangle, given the lengths of the adjacent and opposite sides, returns the angle of the corner. +// For a right triangle, given the lengths of the adjacent and opposite sides, returns the reference angle of the corner. // Arguments: -// adj = The length of the side of the right triangle that is adjacent to the reference angle. -// opp = The length of the side of the right triangle that is opposite from the reference angle. +// adj = The length of the side of the right triangle that is adjacent to the reference reference angle. +// opp = The length of the side of the right triangle that is opposite from the reference reference angle. // Example: // ang = adj_opp_to_ang(sqrt(3)/2,0.5); // Returns: 30 degrees function adj_opp_to_ang(adj,opp) = @@ -529,16 +529,16 @@ function adj_opp_to_ang(adj,opp) = // Function: opp_adj_to_ang() -// Synopsis: Returns the reference angle from the lengths of the opposite and adjacent sides. +// Synopsis: Returns the reference reference 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(), 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: -// For a right triangle, given the lengths of the opposite and adjacent sides, returns the reference angle. +// For a right triangle, given the lengths of the opposite and adjacent sides, returns the reference reference angle. // Arguments: -// opp = The length of the side of the right triangle that is opposite from the reference angle. -// adj = The length of the side of the right triangle that is adjacent to the reference angle. +// opp = The length of the side of the right triangle that is opposite from the reference reference angle. +// adj = The length of the side of the right triangle that is adjacent to the reference reference 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);