# cos

Cosine of argument in radians

## 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 real values of X, cos(X) returns real values in the interval [-1, 1].

• For complex values of X, cos(X) returns complex values.

## Examples

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Plot the cosine function over the domain $-\pi \le x\le \pi$.

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 = 1×3 complex

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, multidimensional array, table, or timetable.

Data Types: single | double | table | timetable
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, multidimensional array, table, or timetable.

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### Cosine Function

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

The cosine of a complex argument, α, is

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

## Tips

• To compute cos(X*pi) accurately, without using pi as a floating-point approximation of π, you can use the cospi function instead. For example, cospi(m/2) is exactly zero for odd integers m and cospi(n) is +1 or –1 for integers n.

## Version History

Introduced before R2006a

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