naginterfaces.library.specfun.arccos

naginterfaces.library.specfun.arccos(x)

arccos returns the value of the inverse circular cosine, $\arccos \left(x\right)$; the result is in the principal range $(0,\pi )$.

For full information please refer to the NAG Library document for s09ab

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/s/s09abf.html

Parameters

xfloat

The argument $x$ of the function.

Returns

acxfloat

The value of the inverse circular cosine, $\arccos \left(x\right)$.

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.

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

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

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

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

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

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

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

References

NIST Digital Library of Mathematical Functions