The ASIN function is used to return the arcsine of a number in radians.

## Contents:

## Syntax

`= ASIN(`*number*)

*number -* The sine value for which you want to calculate the arcsine

*Note: the results will be returned as radians. To return a degree, use the DEGREES function like so:*

`= DEGREES(ASIN(`*number*))

### Explanation

The ASIN function is part of the "Math and Trigonometry" group of functions within Excel.

This function calculates an arcsine which is the inverse of the sine function, and calculates the angle in radians.

Arcsine is used to measure an unknown angel when the hypotenuse and opposite side is known.

## What is Arcsine

To understand arcsine, let's consider the relationship between angles and the ratios of sides in right-angled triangles.

The arcsine of an angle (a) is the ratio of the length of the opposite side (x) to the length of the hypotenuse (y).

Conversely, arcsine (arcsin or ASIN) finds the inverse angle. The inverse of sine is useful when the sine is known, but the angle itself is not.

For example, if the sine of an angle is calculated as:

**a = opposite / hypotenuse = x / y = 26/ 30 â‰ˆ 0.867**, then **a = arcsin(0.867) â‰ˆ 60Â°**.

In trigonometry, every function has an inverse that works in reverse. These inverses are prefixed with 'arc', making the inverse of **sine **the **arcsine**.

### Examples

## How to Calculate Arcsine Using the Hypotenuse and Opposite Side of a Triangle

Let's say we have table representing triangles with two know sides, the hypotenuse and the side opposite to the angle that we want to calculate, and want the answer in degrees.

The formula to calculate the arcsine in degrees would be:

`= DEGREES(ASIN(`*opposite/hypotenuse*))

If we plug this formula into the table, we get the correct arcsine angles (rounded here to the nearest degree).

This table uses the ASIN function to calculate the angle from the given sides of a right-angled triangle, and converts that result into degrees.

If you don't want to use the DEGREES function, you can also multiply the result by **180/pi****.**