sin¶

sin(x:array,/)→array¶

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

Each elementx_i is assumed to be expressed in radians.

Note

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

Note

For complex arguments, the mathematical definition of sine is

\[\begin{split}\begin{align} \operatorname{sin}(x) &= \frac{e^{jx} - e^{-jx}}{2j} \\ &= \frac{\operatorname{sinh}(jx)}{j} \\ &= \frac{\operatorname{sinh}(jx)}{j} \cdot \frac{j}{j} \\ &= -j \cdot \operatorname{sinh}(jx) \end{align}\end{split}\]

where\(\operatorname{sinh}\) is the hyperbolic sine.

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 sine 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 is+0.

• Ifx_i is-0, the result is-0.

• Ifx_i is either+infinity or-infinity, the result isNaN.

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

Changed in version 2022.12:Added complex data type support.