Trig Functions

Trigonometric Functions

Important

Analytica's trigonometric functions operate using degrees, not radians.

Function Radians

Radians(Degrees: atomic numeric)

Converts an angle measure expressed in degrees to the equivalent measure expressed in radians.

Function Degrees

Degrees(Radians: numeric atomic)

Converts an angle measure expressed in radians to an equivalent degree measure.

Functions Cos, Sin and Tan

Basic trigonometric functions. Parameter is in degrees.

Sin(90) → 1

Cos(Degrees(Pi)) → -1

Functions ArcCos, ArcSin, ArcTan, ArcTan2

ArcCos(X: Numeric atomic)

ArcSin(X: Numeric atomic)

ArcTan(X: Numeric atomic)

ArcTan2(Y, X: Numeric atomic)

Inverse trig functions. Results are in Degrees. The range of the results are as follows:

Function	Range (in degrees)
ArcCos	0 to 180
ArcSin	-90 to 90
ArcTan	-90 to 90
ArcTan2	-180 to 180

Note: ArcTan2(0, 0) returns 0.

Functions CosH, SinH, TanH

Hyperbolic trig functions. The parameter is in degrees.

An xy-graph of Sin(x) vs. Cos(x) plots a circle. Analoguously, an xy-graph of SinH(x) vs. CosH(x) plots a hyperbola (on the right side of the y-axis):

Although the parameter is specified in degrees, it does not denote an angle to the point on the hyperbola. «x» is referred to as the hyperbolic angle and is defined to be the area of the hyperbolic sector times [math]\displaystyle{ 360 / \pi }[/math]. Conversely, the area of the hyperbolic sector is [math]\displaystyle{ x \pi / 360 }[/math].

[math]\displaystyle{ CosH(x) = {{e^{Radians(x)} + e^{-Radians(x)}}\over 2} }[/math]

[math]\displaystyle{ SinH(x) = {{e^{Radians(x)} - e^{-Radians(x)}}\over 2} }[/math]

[math]\displaystyle{ TanH(x) = {{e^{Radians(x)} - e^{-Radians(x)}}\over {e^{Radians(x)} + e^{-Radians(x)}}} }[/math]

<math>e^{Radians(x)} = CosH(x) + SinH(x)

<math>e^{Radians(x)} = CosH(x) - SinH(x)

The hyperbolic functions are also defined for complex numbers «x».

Functions ArcCosH, ArcSinH, ArcTanH

Inverse hyperbolic trigonometric functions. The returned value is in degrees.