# Description

Returns the arc sine (aka inverse sine) of an input

Arc sine is the inverse function for sine. That is, given a value for val in the domain [-1.0, 1.0], it will return an angle asin(val) in degrees.

To illustrate, picture the unit circle (a circle of radius 1.0 centered about the origin). If you imagine a unit vector rotating inside of the unit circle, the y-coordinate of the endpoint of the vector is the asin function argument val. The angle that the vector makes with the positive x-axis is the function output asin(val). As the vector rotates inside the circle, the y-coordinate of the vector must always be within the unit circle, so the input argument to asin (aka val) must be within [-1.0, 1.0] to be meaningful.

Also, as sin(t) is doubly valued for t in [-180, 180], the asin function is restricted to quadrant IV and quadrant I. This means that the unit vector rotating inside the unit circle is assumed to have a positive or 0 x-coordinate, therefore asin(val) always returns a value in [-90, 90].

Math

# Command syntax

## Syntax

 `asin value`

### Arguments

`value`floatyesThe domain of arc sine is [-1.0, 1.0]. Values of val outside of this domain are not meaningful to the function asin.

None

## Return value

float

For an input argument val in [-1.0, 1.0], returns a floating point angle (degrees) in the range [-90.0, 90.0]. For input arguments t in the ranges: (1.0, Inf], [-Inf, -1.0) and NaN, asin(t) returns NaN.

## Examples

`float \$t;float \$asin_of_t; float \$sin_of_asin_of_t;// asin(1.0) is 90 degrees because sin(90 degrees) = 1.0\$t                = 1.0;\$asin_of_t        = asin(\$t);\$sin_of_asin_of_t = sin(\$asin_of_t);print("t, asin(t), sin(asin(t)) = " + string(\$t) + ", " + string(\$asin_of_t) + ", " + string(\$sin_of_asin_of_t));// 1.1 is not a meaningful input into asin and will return // NaN (-1.#IND00)\$t = -1.1;\$asin_of_t        = asin(\$t);\$sin_of_asin_of_t = sin(\$asin_of_t);print("t, asin(t), sin(asin(t)) = " + string(\$t) + ", " + string(\$asin_of_t) + ", " + string(\$sin_of_asin_of_t));`