Trigonometry

The Trigonometric Functions defined in the OpenGL 4.6 Shading Language Specification.

#include <fennec/math/trigonometric.h> 

Angle Conversions

Syntax	Description
genFType degrees(genFType x)	Converts \(radians\) to \(degrees\), i.e., \(radians\cdot\frac{\pi}{180}\). Returns the angle \(\theta\) in \(degrees\) Converts \(radians\) to \(degrees\), i.e., \(radians\cdot\frac{\pi}{180}\) Template Parameters genType floating point type Parameters radians the angle \(\theta\) in \(radians\)
genFType radians(genFType x)	Converts \(degrees\) to \(radians\), i.e., \(degrees\cdot\frac{180}{\pi}\). Returns the angle \(\theta\) in \(radians\) Converts \(degrees\) to \(radians\), i.e., \(degrees\cdot\frac{180}{\pi}\) Template Parameters genType floating point type Parameters degrees the angle \(\theta\) in \(degrees\)

Trigonometric Functions

Syntax	Description
genFType sin(genFType x)	The standard trigonometric sine. Returns the sine of \(\theta\) in the range \(\left[-1,\,1\right]\) The standard trigonometric sine Template Parameters genType floating point type Parameters x the angle \(\theta\) in \(radians\)
genFType cos(genFType x)	The Standard Trigonometric Cosine. Returns the cosine of \(\theta\) in the range \(\left[-1,\,1\right]\) The Standard Trigonometric Cosine Template Parameters genType floating point type Parameters x the angle \(\theta\) in \(radians\)
genFType tan(genFType x)	The Standard Trigonometric Tangent. Returns The Tangent of \(\theta\) in the Range \(\left[-\inf,\,\inf\right]\) The Standard Trigonometric Tangent Template Parameters genType floating point type Parameters x The Angle \(\theta\) in \(radians\)
genFType asin(genFType x)	Arc Sine. Returns an angle \(\theta\) whose sine is /a x. Returns an angle \(\theta\) whose sine is /a x. Arc Sine. The range of values returned by this functions is \(\left[-\pi/2,\pi/2\right]\). Results are undefined if \(\left|x\right|\,>\,1\). Template Parameters genType floating point type Parameters x The Sine Value produced by \(\theta\)
genFType acos(genFType x)	Arc Cosine. Returns an angle \(\theta\) whose cosine is /a x. Returns an angle \(\theta\) whose cosine is /a x. Arc Cosine. The range of values returned by this functions is \(\left[0,\pi\right]\). Results are undefined if \(\left|x\right|\,>\,1\). Template Parameters genType floating point type Parameters x The Cosine Value produced by \(\theta\)
genFType atan(genFType x)	Arc Tangent. Returns an angle \(\theta\) whose tangent is /a y_over_x. Returns an angle \(\theta\) whose tangent is /a y_over_x. Arc Tangent. The range of values returned by this functions is \(\left[\frac{-\pi}{2},\frac{\pi}{2}\right]\). Results are undefined if \(\left|x\right|\,>\,1\). Template Parameters genType floating point type Parameters y_over_x The Cosine Value produced by \(\theta\)

Hyperbolic Functions

Syntax	Description
genFType sinh(genFType x)	Returns the Hyperbolic Sine Function, \(\frac{{e}^{x}-{e}^{-x}}{2}\). Returns The Hyperbolic Sine of \(x\), \(\frac{{e}^{x}-{e}^{-x}}{2}\) Template Parameters genType floating point type Parameters x The Hyperbolic Angle \(\alpha\)
genFType cosh(genFType x)	Returns the Hyperbolic Cosine Function, \(\frac{{e}^{x}+{e}^{-x}}{2}\). Returns The Hyperbolic Cosine of \(x\), \(\frac{{e}^{x}+{e}^{-x}}{2}\) Parameters x The Hyperbolic Angle \(\alpha\)
genFType tanh(genFType x)	Returns the Hyperbolic Tangent Function, \(\frac{\text{sinh}(x)}{\text{cosh}(x)}\). Returns The Hyperbolic Tangent of \(x\), \(\frac{{e}^{x}+{e}^{-x}}{2}\) Parameters x The Hyperbolic Angle \(\alpha\)
genFType asinh(genFType x)	The Inverse Hyperbolic Sine Function. Returns the value \(y\) that fulfills \(x=\text{sinh}(y)\) The Inverse Hyperbolic Sine Function Parameters x the hyperbolic angle \(\alpha\)
genFType acosh(genFType x)	The Inverse Hyperbolic Cosine Function. Returns the value \(y\) that fulfills \(x=\text{cosh}(y)\) The Inverse Hyperbolic Cosine Function Parameters x the hyperbolic angle \(\alpha\)
genFType atanh(genFType x)	The Inverse Hyperbolic Tangent Function. Returns the value \(y\) that fulfills \(x=\text{atanh}(y)\) The Inverse Hyperbolic Tangent Function Parameters x The Hyperbolic Angle \(\alpha\)