# MySQL ASIN() – Find the arcsine of a number in MySQL

In this tutorial, we will study the MySQL `ASIN()` function. In maths, you must have come across the function – asin. The arcsine of a number x is the inverse sine function of x where x is a number between -1 and 1. Like all other trigonometric operations, asin is widely used and thatâ€™s why MySQL provides us with the `ASIN()` function. `ASIN()` returns the arcsine of a number. As evident, it is the inverse of the `SIN()` function. `ASIN()` returns the angle whose sine value is passed a parameter to it. Let us dive into the syntax and examples of `ASIN()` now.

## Syntax of MySQL ASIN()

```ASIN(number);
```

Where â€˜numberâ€™ is a number whose arcsine is to be found. Note that, â€˜numberâ€™ should have a value between -1 and 1.

## Examples of MySQL ASIN()

Let us start with some basic examples now. We have the following three expressions – asin 0.2, asin 1 and asin -1. We will find their values in MySQL using the `ASIN()` function with the `SELECT` statement.

```SELECT ASIN(0.2);
SELECT ASIN(1);
SELECT ASIN(-1);
```

And we get the output as,

### MySQL ASIN() With Numbers Out Of Range

Now earlier I mentioned a couple of times that the â€˜numberâ€™ parameter should be a value between -1 (inclusive) and 1 (inclusive). But, what if you pass a value that is not in this range? Let us see that using the below example.

```SELECT ASIN(5);
SELECT ASIN(-15);
```

And the output is,

When we pass numbers not in the range -1 and 1 to `ASIN()`, it returns NULL.

### MySQL ASIN() With Expressions

We can also pass mathematical expressions as parameters inside the `ASIN()` function. Suppose you have the following two expressions – asin (0.5+0.2) and asin (0.5*0.3). We can do this in MySQL using the `ASIN()` using the below queries.

```SELECT ASIN(0.5+0.2);
SELECT ASIN(0.5*0.3);
```

And the output is,

### MySQL ASIN() With Zero and NULL

The arcsine of zero is zero. We can demonstrate this in MySQL using the below example.

```SELECT ASIN(0);
```

And the output is,

`ASIN()` returns NULL if the number passed to it is NULL. We can demonstrate this using the below example.

```SELECT ASIN(NULL);
```

And we get the output as follows –

### ASIN() Is The Inverse Of SIN()

As mentioned earlier in the introduction, `ASIN()` is the inverse of `SIN()`. Suppose the sine of y is equal to x. That is,

`sin y = x`

Then the arcsine of x is equal to the inverse sine function of x, which is therefore, equal to y:

`arcsin x = sin-1 x = y`

Let us demonstrate this using the below example.

```SELECT ASIN(SIN(0.5));
```

First, we get the value of `SIN(0.5)` which is roughly 0.479. Now the result of the `SIN()` function is passed into the `ASIN()` function. Since `ASIN()` is the inverse of `SIN()`, it will return the numerical value that was passed to the `SIN()` function (0.5 in this example) as the result. Therefore, we get the output as follows –

### Using ASIN() With Tables

Consider the below â€˜Anglesâ€™ table.

Building on the previous example about how `ASIN()` is the inverse of `SIN()`, let us write a query that displays the `Angle` column and the arcsine of the values in the `SineOfAngle` column. We use aliases to make our output readable. The query is –

```SELECT Angle, ASIN(SineOfAngle) AS Arcsine FROM Angles;
```

And the output is,

As you can see, the values in both columns are equal to each other.

## Conclusion

Finding the arcsine of an angle is an important trigonometric operation. You will find yourself using the `ASIN()` function every time you deal with data with trigonometric operations.