# tan

## Description

example

Y = tan(X) returns the tangent of each element of X. The tan function operates element-wise on arrays. The function accepts both real and complex inputs. For real values of X in the interval [-Inf, Inf], tan returns real values in the interval [-Inf ,Inf]. For complex values of X, tan returns complex values. All angles are in radians.

## Examples

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### Plot Tangent Function

Plot the tangent function over the domain .

x = (-pi/2)+0.01:0.01:(pi/2)-0.01; plot(x,tan(x)), grid on 

### Tangent of Vector of Complex Angles

Calculate the tangent of the complex angles in vector x.

x = [-i pi+i*pi/2 -1+i*4]; y = tan(x) 
y = 0.0000 - 0.7616i -0.0000 + 0.9172i -0.0006 + 1.0003i 

## Input Arguments

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### X — Input angle in radiansnumber | vector | matrix | multidimensional array

Input angle in radians, specified as a number, vector, matrix, or multidimensional array.

Data Types: single | double
Complex Number Support: Yes

## Output Arguments

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### Y — Tangent of input anglescalar value | vector | matrix | N-D array

Tangent of input angle, returned as a real-valued or complex-valued scalar, vector, matrix or N-D array.

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### Tangent Function

The tangent of an angle, α, defined with reference to a right angled triangle is

.

The tangent of a complex angle, α, is

$\text{tan}\left(\alpha \right)=\frac{{e}^{i\alpha }-{e}^{-i\alpha }}{i\left({e}^{i\alpha }+{e}^{-i\alpha }\right)}\text{\hspace{0.17em}}.$

.