# Documentation

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# sin

Y = sin(X)

## Description

example

Y = sin(X) returns the sine of the elements of X. The sin function operates element-wise on arrays. The function accepts both real and complex inputs. For real values of X in the interval [-Inf, Inf], sin returns real values in the interval [-1 ,1]. For complex values of X, sin returns complex values. All angles are in radians.

## Examples

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Plot the sine function over the domain .

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

Calculate the sine of the complex angles in vector x.

x = [-i pi+i*pi/2 -1+i*4];
y = sin(x)
y = 1×3 complex

0.0000 - 1.1752i   0.0000 - 2.3013i -22.9791 +14.7448i

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

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### Sine Function

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

The sine of a complex angle, α, is

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