# cot

## Syntax

• Y = cot(X)
example

## Description

example

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

## Examples

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### Plot Cotangent Function

Plot the cotangent function over the domain and .

x1 = -pi+0.01:0.01:-0.01; x2 = 0.01:0.01:pi-0.01; plot(x1,cot(x1),x2,cot(x2)), grid on 

### Cotangent of Vector of Complex Angles

Calculate the cotangent of the complex angles in vector x.

x = [-i pi+i*pi/2 -1+i*4]; y = cot(x) 
y = 0.0000 + 1.3130i -0.0000 - 1.0903i -0.0006 - 0.9997i 

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

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

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### Cotangent Function

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

.

The cotangent of a complex angle α is

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

.