# MySQL SIN() – How to find the sine of angles in MySQL? In this tutorial, we will learn about the MySQL `SIN()` function. While studying high school mathematics, you must have studied how to find the sine of an angle. Finding the sine of a number is an important trigonometric operation which finds use in mathematics, physics and so on. MySQL provides us with the `SIN()` function to find the sine of a value where the value is given in radians. Let us look at the syntax of the `SIN()` function followed by some examples.

## Syntax of MySQL SIN()

```SIN(number);
```

Where ‘number’ is a value in radians whose sine is to be found.

## Examples of MySQL SIN()

Let’s kick things off with a couple of basic examples of MySQL `SIN()`. Let us find the sine of 5, 120 and 3. Our queries are –

```SELECT SIN(5);
SELECT SIN(120);
SELECT SIN(3);
```

And the output is,

### MySQL SIN() With Negative Values

We can also use negative values with the `SIN()` function. Let us demonstrate this using the following queries.

```SELECT SIN(-5);
SELECT SIN(-120);
SELECT SIN(-3);
```

And the output is,

### SIN() Of PI()

We can also pass a function within `SIN()`. Let us find the sine of 𝜋 using the `PI()` function. We do this using the below query.

```SELECT SIN(PI());
```

And the output is,

### Using Expressions with MySQL SIN()

We can also use expressions with the `SIN()` function. Suppose we have the following expression:

1 – sin 𝜋/6

We do this using the below query,

```SELECT 1-SIN(PI()/6);
```

First, the `PI()`/6 expression is evaluated. Next, the expression finds the sine of the resulting value and then subtracts it from 1. We get the output as,

### POW() with SIN()

One of the mathematical functions you’ll find using the most with the `SIN()` function is `POW()`. Let us take this opportunity to see an example of the same. Consider the below expression.

sin2 1.5

We solve this using the below query.

```SELECT POW(SIN(1.5), 2);
```

First, the `SIN()` function gets evaluated. And then, we square the resulting value with the `POW()` function. Finally, we get the output as follows.

## SIN() With Tables

Consider the below ‘Angles’ table. The Angles Table contains the ID of an angle and its value in radians.

Using the `SELECT` statement, the `SIN()` function and an alias called `SineOfAngle`, let us display the table along with the sine of every corresponding angle. We do this using the below query.

```SELECT ID, Angle, SIN(Angle) AS SineOfAngle FROM Angles;
```

And we get the output as follows,

### UPDATE Statement With SIN()

Let us now create a column called SineOfAngle which stores the sine of every angle in the Angles table. We will use the `ALTER` and `UPDATE` statements for this task. Let us take a look at the queries.

```ALTER TABLE Angles ADD SineOfAngle float;
UPDATE Angles SET SineOfAngles=SIN(Angle);
SELECT * FROM Angles;
```

We add a column named SineOfAngle of the data type float using the `ALTER` statement. Next, using the `UPDATE` statement, we populate the `NULL` values in the SineOfAngle column with the sine of the angles from the Angle column. Finally, using the `SELECT` statement, we display our newly updated table. The output is as follows.

### A Complex Example

Okay. If you have studied trigonometric formulas, you must have definitely come across the below formula.

`sin 3A = 3sin A - 4sin3 A`

Complicated, I know. So how about proving if this formula is true using the ‘Angles’ table and the `SIN()` function. Bear with me because we are gonna be writing a really complicated query using all the concepts we saw earlier.

```SELECT 3*SIN(Angle), 3*SIN(Angle)-4*POW(SIN(Angle), 3) FROM Angles;
```

The first part of the above query is used to evaluate the ‘sin 3A’ part of the formula. The second part of the `SELECT` statement is used to evaluate ‘3sin A – 4sin3 A’. Read the query once more to understand it better by breaking it one value at a time.

We get the output as,

As you can see, the values in both columns match. Hence, we proved the formula is true using MySQL `SIN()`.

## Conclusion

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