## Purpose

## Return value

## Arguments

*number*- The angle in radians for which you want the sine.

## Syntax

## Usage notes

The SIN function returns the sine of an angle provided in radians. In geometric terms, the sine of an angle returns the ratio of a right triangle's opposite side over its hypotenuse. For example, the sine of PI()/6 radians (30°) returns the ratio 0.5.

```
=SIN(PI()/6) // Returns 0.5
```

### Using Degrees

To supply an angle to SIN in degrees, multiply the angle by PI()/180 or use the RADIANS function to convert to radians. For example, to get the SIN of 30 degrees, you can use either formula below:

```
=SIN(30*PI()/180)
=SIN(RADIANS(30))
```

### Explanation

The graph of sine, shown above, visualizes the output of the function for all angles from 0 to a full rotation. The function is periodic, so after a full rotation, the output of the function repeats. Geometrically, the function returns the *y*-component of the point corresponding to an angle on the unit circle. The function's output will always be in the range [-1, 1].

*Graph courtesy of wumbo.net.*