# TAN

The `TAN` function returns the tangent of an angle specified in radians. Tangent is the ratio of the length of the opposite side to the length of the adjacent side of a right-angled triangle. This function is commonly used in trigonometry and geometry calculations.

## Usage

Use the `TAN` formula with the syntax shown below, it has 1 required parameter:

Parameters:
1. angle (required):
The angle in radians for which you want to calculate the tangent. Must be a real number.

## Examples

Here are a few example use cases that explain how to use the `TAN` formula in Google Sheets.

### Calculate the height of an object

If you know the angle of elevation and the distance from the object, you can use the `TAN` function to calculate the height of the object. For example, if you measure a 30 degree angle of elevation to the top of a tree that is 50 feet away, you can use the formula `=TAN(RADIANS(30))*50` to find that the tree is approximately 28.87 feet tall.

### Calculate the slope of a hill

You can use the `TAN` function to calculate the slope of a hill or incline. For example, if you measure a 10 degree angle of incline, you can use the formula `=TAN(RADIANS(10))` to find that the slope is approximately 0.176.

### Calculate the period of a pendulum

You can use the `TAN` function to calculate the period of a pendulum. For example, if you know the length of the pendulum and the acceleration due to gravity, you can use the formula `=2*PI()*SQRT(length/g)` to find the period of the pendulum, where `g` is the acceleration due to gravity, and `length` is the length of the pendulum. You can use the `TAN` function to calculate the angle of displacement of the pendulum from its equilibrium position.

## Common Mistakes

`TAN` not working? Here are some common mistakes people make when using the `TAN` Google Sheets Formula:

The TAN function in Google Sheets uses radians as its input. If you provide an angle in degrees, you need to convert it to radians first by multiplying it by pi/180 or using the RADIANS function.

### Dividing by zero

If you provide an angle that is a multiple of 90 degrees, the TAN function will return an error because the tangent of 90 degrees or any multiple of it is undefined (infinite).

### Forgetting to close parentheses

Make sure you close the parentheses in the TAN function after you provide the angle. Not doing so will result in a syntax error.

The following functions are similar to `TAN` or are often used with it in a formula:

• `SIN`

The `SIN` function in Google Sheets returns the sine of a given angle in radians. Sine is a mathematical function that describes a smooth repetitive oscillation. It is commonly used in trigonometry, physics, and engineering to model phenomena such as waves, oscillations, and periodic motion.

• `COS`

The `COS` function in Google Sheets returns the cosine of an angle provided in radians. It is commonly used in trigonometry to calculate the cosine of an angle. The function takes one parameter, the angle in radians.

• `ATAN`

The `ATAN` function returns the arctangent of a value in radians, which is the angle whose tangent is a given value. This function is commonly used in trigonometry and geometry to calculate angles. The returned angle is in the range -π/2 to π/2.

• `ASIN`

The ASIN function returns the arcsine of a value in radians, which is the angle whose sine is the specified value. This function is commonly used in trigonometry and geometry calculations. When used in a formula, the ASIN function takes a single argument, the value for which to calculate the arcsine.

You can learn more about the `TAN` Google Sheets function on Google Support.