cos¶

cos(x:array,/)→array¶

Calculates an implementation-dependent approximation to the cosine for each elementx_i of the input arrayx.

Each elementx_i is assumed to be expressed in radians.

Note

The cosine is an entire function on the complex plane and has no branch cuts.

Note

For complex arguments, the mathematical definition of cosine is

\[\begin{split}\begin{align} \operatorname{cos}(x) &= \sum_{n=0}^\infty \frac{(-1)^n}{(2n)!} x^{2n} \\ &= \frac{e^{jx} + e^{-jx}}{2} \\ &= \operatorname{cosh}(jx) \end{align}\end{split}\]

where\(\operatorname{cosh}\) is the hyperbolic cosine.

Parameters:

x (array) – input array whose elements are each expressed in radians. Should have a floating-point data type.

Returns:

out (array) – an array containing the cosine of each element inx. The returned array must have a floating-point data type determined byType Promotion Rules.

Notes

Special cases

For real-valued floating-point operands,

• Ifx_i isNaN, the result isNaN.

• Ifx_i is+0, the result is1.

• Ifx_i is-0, the result is1.

• Ifx_i is+infinity, the result isNaN.

• Ifx_i is-infinity, the result isNaN.

For complex floating-point operands, special cases must be handled as if the operation is implemented ascosh(x*1j).

Changed in version 2022.12:Added complex data type support.