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# sin

## Syntax

``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 argument, α, is

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