sin

sin(x: array, /) → array

Calculates an implementation-dependent approximation to the sine for each element x_i of the input array x.

Each element x_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 in x. The returned array must have a floating-point data type determined by Type Promotion Rules.

Notes

Special cases

For real-valued floating-point operands,

• If x_i is NaN, the result is NaN.

• If x_i is +0, the result is +0.

• If x_i is -0, the result is -0.

• If x_i is either +infinity or -infinity, the result is NaN.

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.