naginterfaces.library.specfun.arcsin

naginterfaces.library.specfun.arcsin(x)

arcsin returns the value of the inverse circular sine, $\arcsin \left(x\right)$. The value is in the principal range $(-\pi /2,\pi /2)$.

For full information please refer to the NAG Library document for s09aa

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/s/s09aaf.html

Parameters

xfloat

The argument $x$ of the function.

Returns

asxfloat

The value of the inverse circular sine, $\arcsin \left(x\right)$.

Raises

NagValueError

(errno $1$)

On entry, $x=⟨value⟩$.

Constraint: $\left|x\right|\le 1$.

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

arcsin calculates an approximate value for the inverse circular sine, $\arcsin \left(x\right)$. It is based on the Chebyshev expansion

$$\arcsin \left(x\right)=x\times y\left(x\right)=x{\sum ^{\prime }}_{r=0}{a}_r{T}_r\left(t\right)$$

where $-\frac{1}{\sqrt{2}}\le x\le \frac{1}{\sqrt{2}}$ and $t=4x^2-1$.

For $x^2\le \frac{1}{2}\text{,}\arcsin \left(x\right)=x\times y\left(x\right)$.

For $\frac{1}{2}<x^2\le 1\text{,}\arcsin \left(x\right)=sign\left(x\right)\{\frac{\pi }{2}-\arcsin \left(\sqrt{1-x^2}\right)\}$.

For $x^2>1\text{,}\arcsin \left(x\right)$ is undefined and the function fails.

References

NIST Digital Library of Mathematical Functions