In this tutorial, we will study the MySQL `ATAN()`

and `ATAN2()`

functions. In high school, you must have studied the arc tangent of an angle in trigonometry. Since trigonometry is so widely used across a number of fields, MySQL provides us with the MySQL `ATAN()`

and `ATAN2()`

functions.

The `ATAN()`

function is used to find the arc tangent of a value. It can also return the arc tangent of two values.

The `ATAN2()`

function is used to find the arc tangent of two values. The two values are provided as comma-separated arguments and the function returns the arc tangent value of argument1 divided by argument2.

*Recommended Read – MySQL TAN() and COS() functions*

Table of Contents

## Syntax of MySQL ATAN()

```
ATAN(number);
```

Where ‘number’ is the value of an angle (in radians) whose arc tangent has to be found out.

OR

```
ATAN(X, Y);
```

Where ‘X’ is the first number and ‘Y’ is the second number and the function returns the arc tangent of the value ‘X/Y’.

## Syntax of MySQL ATAN2()

```
ATAN2(X, Y);
```

Where ‘X’ is the first number and ‘Y’ is the second number and the function returns the arc tangent of the value ‘X/Y’.

## Example of MySQL ATAN()

Let us start by looking at some basic examples of the `ATAN()`

function. Consider the below queries.

```
SELECT ATAN(2.3);
SELECT ATAN(1);
SELECT ATAN(0.052);
```

And we get the output as –

### ATAN() With Negative Values

We can also pass negative values in the `ATAN()`

function. Let us see a few examples of this. Consider the below queries.

```
SELECT ATAN(-9);
SELECT ATAN(-3.2);
SELECT ATAN(-1);
```

And we get the output as –

### ATAN() With Expressions

We can also pass mathematical expressions as parameters to the `ATAN()`

function. Let us see an example of this using the below queries.

```
SELECT ATAN(3.8+0.0056);
SELECT ATAN(0.2*0.06);
```

And we get the output as follows.

### ATAN() With Two Arguments

Now let us try using the second syntax of the `ATAN()`

function where we can pass two arguments. Consider the below queries.

```
SELECT ATAN(6, 2);
SELECT ATAN(0.2, 5);
SELECT ATAN(-5, 8);
```

These queries will return the arc tangent of the values – 6/2, 0.2 / 5, and -5/8. The output is –

To get more clarity, let us see the below example. Since 6 divided by 2 = 3, we will find the arctangent of 3 and then the arctangent of 6/2 using the two-argument syntax of `ATAN()`

. Consider the query –

```
SELECT ATAN(6, 2), ATAN(3);
```

And we get the output as –

Therefore, when two arguments X and Y are passed to `ATAN()`

, it returns the arc tangent of the value X/Y.

### ATAN() With PI()

We can also pass mathematical functions like `MySQL PI()`

to `ATAN()`

. Consider the below query.

```
SELECT ATAN(PI()/2);
```

And we get the output as –

## Examples of MySQL ATAN2()

Let us now move on to some of the basic examples of MySQL `ATAN2()`

. Consider the below queries.

```
SELECT ATAN2(3, 2);
SELECT ATAN2(6, 2);
```

The function returns the arc tangent of the values 3/2 and 6/2 respectively. And we get the output as –

### Similarity of ATAN2() and ATAN() With Two Arguments

`ATAN()`

with two arguments is equal to the `ATAN2()`

function. However, we highly recommend you to use `ATAN2()`

when dealing with two values.

Let us now see how `ATAN()`

with two arguments is similar to `ATAN2()`

. Suppose we have to find the arctangent of 6/2. We can do this in three ways.

First, we reduce 6/2 to 3 and pass 3 as a single argument to `ATAN()`

. Second, we can pass 6 and 2 as two arguments to the `ATAN()`

function, and lastly, we can pass 6 and 2 to the `ATAN2()`

function. Let us see the query for this.

```
SELECT ATAN(3), ATAN(6, 2), ATAN2(6, 2);
```

And we get the output as –

### ATAN2() With Negative Values

We can also pass negative values to the `ATAN2()`

function. Consider the below queries.

```
SELECT ATAN2(-5, 6);
SELECT ATAN2(-3, 5);
SELECT ATAN2(8, -2);
```

And we get the output as follows –

### ATAN2() With PI()

We can also pass mathematical functions like `PI()`

to the `ATAN2()`

function. Let us see an example of this.

```
SELECT ATAN2(PI(), 4);
```

And we get an output as follows.

## Using ATAN() and ATAN2() With Tables

Consider the below ‘Angles’ table.

### MySQL ATAN() Example With Tables

Let us display the Angle column and the corresponding arc tangent value of the angle under the alias ArcTangent using the SELECT statement. The query is –

```
SELECT Angle, ATAN(Angle) AS ArcTangent FROM Angles;
```

And we get the output as follows –

### MySQL ATAN2() Example With Tables

Lastly, let us display the Angle column and the arc tangent of half the angle value in the Angle column. The query for this is –

```
SELECT Angle, ATAN2(Angle, 2) AS ‘ArcTangent/2’ FROM Angles;
```

And we get the output as –

## Conclusion

Finding the arc tangent of an angle is an important trigonometric operation. You will find yourself using the `ATAN()`

and `ATAN2()`

functions every time you deal with data with trigonometric operations. Prefer using `ATAN2()`

when dealing with two values and `ATAN()`

when using a single value.

## References

- MySQL Official Documentation on
`ATAN()`

and`ATAN2()`

.