# Documentation

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# cos

Cosine of argument in radians

## Syntax

• Y = cos(X)

## Description

Y = cos(X) returns the cosine for each element of X. The cos function operates element-wise on arrays. The function accepts both real and complex inputs. For purely real values or imaginary values of X, cos returns real values in the interval [-1 ,1]. For complex values of X, cos returns complex values. All angles are in radians.

## Examples

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Plot the cosine function over the domain .

x = -pi:0.01:pi; plot(x,cos(x)) grid on 

Calculate the cosine of the complex angles in vector x.

x = [-i pi+i*pi/2 -1+i*4]; y = cos(x) 
y = 1.5431 + 0.0000i -2.5092 - 0.0000i 14.7547 +22.9637i 

## Input Arguments

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

Data Types: single | double
Complex Number Support: Yes

## Output Arguments

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Cosine of input angle, returned as a real-valued or complex-valued scalar, vector, matrix or multidimensional array.

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### Cosine Function

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

The cosine of a complex angle, α, is

$\text{cos}\left(\alpha \right)=\frac{{e}^{i\alpha }+{e}^{-i\alpha }}{2}\text{\hspace{0.17em}}.$

### Tall Array Support

This function fully supports tall arrays. For more information, see Tall Arrays.