# Tan-1 Calculator

Table of contents

What is tan-1 in math?What is the notation for the inverse of tangent?How to use this tan-1 calculator?Omni tools related to this topicFAQsThe tan-1 calculator is here to help whenever you struggle with equations of the form `tan-1(x) = y`

. We're here to help you understand what these equations mean and how to solve them.

## What is tan-1 in math?

The notation tan-1 may mean two different things in math:

**tan-1(x) = 1/tan(x) = cot(x)**, i.e., we deal here with the multiplicative inverse; or**tan-1(x) = arctan(x)**, so the**inverse function of the tangent**. We're answering here the question of*what is the angle whose tangent is equal to*.**x**

People who write **tan-1** most often have in mind the latter meaning: why would you bother typing tan-1(x) if you can just write cot(x)? However, sometimes you'll need to guess from the context.

As you can see, the notation tan-1 can be extremely confusing and you should avoid it. If you mean the cotangent, use `cot(x)`

. What should you use for the inverse of tangent? We'll discuss it now.

## What is the notation for the inverse of tangent?

The **most common** notation for the inverse of the tangent is `arctan(x)`

. The prefix `arc`

has its roots in the fact that when using a unit circle and measuring angles in radians, an angle of `x`

radians will correspond to an arc whose length is also `x`

. Hence, "the angle whose tangent is x" coincides with **"the arc whose tangent is x"**.

In **programming languages**, the inverse of tangent is often shortened to `atan(x)`

.

## How to use this tan-1 calculator?

This tan-1 calculator is a very straightforward tool to use. Just **input a number** in the field and enjoy seeing the results in the blink of an eye!

For instance, if you need to determine `tan-1(3)`

, just type `3`

in the field `x`

. You'll see that the result is `1.2490`

radians, so a bit more than `71.5°`

. Note that the calculator allows you to ***convert between radians and degrees**. You don't need to do that by hand or look for additional tools!

### How do I find the tan-1 of negative numbers?

To determine the tan-1 of a negative number, follow these steps:

- Write down the
**absolute value**of your number. In other words, get rid of the minus sign. - Find the tan-1 of the absolute value you've found in Step 1.
- Take the result and write the minus sign in front of it. Formally: find the
**opposite number**. - This is your result! We've applied here the formula
`tan-1(-x) = -tan-1(x)`

for every real number`x`

.

### What is the tan-1 of -1?

**The answer is -45°, or equivalently, -π/4 rad.** To arrive at this result, you must use the formula

`tan-1(-x) = -tan-1(x)`

. Plugging in `x = -1`

, we obtain `tan-1(-1) = - tan-1(1)`

and so it suffices to recall that `tan(π/4) = 1`

.