In this tutorial, we will learn about the MySQL `TAN()`

function. While studying high school mathematics, you must have studied how to find the tangent of an angle. Finding the tangent of an angle is an important trigonometric operation that finds use in mathematics, physics, and so on.

*Recommended read – MySQL SIN() – MySQL ASIN() – MySQL COS()*

MySQL provides us with the `TAN()`

function to find the tangent of a value where the value is given in radians. It is important to note that we can also get the tangent of an angle by dividing the sine of an angle with the cosine of an angle.

Table of Contents

## Syntax of MySQL TAN()

```
TAN(number);
```

Where ‘number’ is the measure of an angle in radians whose tangent is to be found.

## Examples of MySQL TAN()

Let us start with some basic examples. How about we find the tangent of the following – 2.2, 45, and 1. We use the below queries for the same.

```
SELECT TAN(2.2);
SELECT TAN(45);
SELECT TAN(1);
```

And we get the output as,

### MySQL TAN() With Negative Values

We can also pass negative values to the MySQL `TAN()`

function. Let us see this using the below examples.

```
SELECT TAN(-0.2);
SELECT TAN(-0.75);
SELECT TAN(-50);
```

And we get the output as follows.

### MySQL TAN() With PI()

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

as arguments to the `TAN()`

function. Most of the times, radian values are expressed in terms of 𝜋. Let us see an example of the `TAN()`

function when `PI()`

is passed to it as an argument.

```
SELECT TAN(PI());
```

And the output is,

### MySQL TAN() With Expressions

In addition to mathematical functions, we can also pass expressions as arguments to `TAN()`

. We can also include `TAN()`

in expressions. Consider the below expression.

1 + 3 tan 𝜋/4

Let us write a query for the above expression using the `TAN()`

function in MySQL.

```
SELECT 1+3*TAN(PI()/4);
```

And the output is,

## Using MySQL TAN() With Tables

Consider the below ‘Angles’ table. The Angle column contains the measure of angles in radians.

### Simple Example

You must have studied in school that the tangent of an angle is the sine of an angle divided by the cosine of an angle. Mathematically, this is given as –

tan x = sin x / cos x

Let us write a query in which the first part divides the values in the column `SineOfAngle`

with the values in the column `CosineOfAngle`

. The result should have an alias `TangentOfAngle`

. The second part of the same query should find the tangent of the values in the Angle column using the `TAN()`

function. The alias for this result should be `TAN_OfAngle`

. The query is –

```
SELECT SineOfAngle/CosineOfAngle AS TangentOfAngle, TAN(Angle) AS TAN_OfAngle FROM Angles;
```

And we get the output as follows –

### TAN() With The UPDATE Statement

Let us now create a column called `TangentOfAngle`

which stores the tangent 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 TangentOfAngle float;
UPDATE Angles SET TangentOfAngle=TAN(Angle);
SELECT * FROM Angles;
```

We add a column named `TangentOfAngle`

with the data type float using the `ALTER`

statement. Next, using the `UPDATE`

statement, we populate the NULL values in the `TangentOfAngle`

column with the tangent of the angle values from the Angle column. Finally, using the `SELECT`

statement, we display our newly updated table. The output is as follows.

### A Complex Example

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

tan 2A = (2 tan A) / (1 – tan2 A)

How about proving if this formula is true using the ‘Angles’ table and the `TAN()`

function. Bear with me because we are gonna be writing a complicated query using all the concepts we saw earlier. We will give ‘tan 2A’ an alias called LHS and ‘ 2 tan A / 1 – tan2 A’ an alias called RHS.

```
SELECT TAN(2*Angle) AS LHS, (2*TAN(Angle))/(1-POW(TAN(Angle),2)) AS RHS FROM Angles;
```

Read the query once more to understand it better by breaking it one term at a time. We get the output as,

## Conclusion

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

function every time you deal with data with trigonometric operations.

## References

- MySQL Official Documentation on
`TAN()`

.