tan

tan(x: array, /) → array

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

Each element x_i is assumed to be expressed in radians.

Note

Tangent is an analytical function on the complex plane and has no branch cuts. The function is periodic, with period $\pi j$, with respect to the real component and has first order poles along the real line at coordinates $(\pi (\frac{1}{2}+n),0)$. However, IEEE 754 binary floating-point representation cannot represent the value $\pi /2$ exactly, and, thus, no argument value is possible for which a pole error occurs.

Note

For complex arguments, the mathematical definition of tangent is

$$\begin{array}{r}\begin{array}{rl}\tan (x)& =\frac{j(e^{-jx}-e^{jx})}{e^{-jx}+e^{jx}}\\ & =(-1)\frac{j(e^{jx}-e^{-jx})}{e^{jx}+e^{-jx}}\\ & =-j\cdot \tanh (jx)\end{array}\end{array}$$

where $\tanh$ is the hyperbolic tangent.

Parameters:

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

Returns:

out (array) – an array containing the tangent 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 * tanh(x*1j).

Changed in version 2022.12: Added complex data type support.