# Cos-1 Calculator

Table of contents

What is cos-1 in math?How do I invert the cosine function?How to use this cos-1 calculator?FAQsWelcome to Omni's cos-1 calculator! It is here to help you solve problems connected to the inverse of the cosine function. All you need to do is to input a number and grab the result! Wanna learn more about the role of cos-1 in math? We've prepared a brief explanation - scroll down!

## What is cos-1 in math?

Beware - the notation **cos-1** have two very different meanings:

**cos-1(x) = 1/cos(x)**, i.e., the**multiplicative inverse**of cos(x); or**cos-1(x) = arccos(x)**, i.e., the**inverse function of the cosine**. In other words, we have the problem of*determining the angle whose cosine equals*.**x**

We assume that you have in mind the inverse cosine.

## How do I invert the cosine function?

The inverse of the cosine function is most often denoted by `arccos`

. It answers the question of what angle leads to a particular value of cosine:

**arccos(x) = y if and only if x = cos(y)**.

Looks easy, isn't it? However, there's a small trap! Namely, you can only calculate `arccos`

for numbers in the interval **[-1, 1]**, because cosine assumes only values between -1 and 1.

Look at the graph of the cos-1 function: you can see its domain.

In the graph, we also see that the **range of arccos** is the interval [0, π] (in radians: it equals the range [0,180°] in degrees). This is because the cosine is a periodic function; in particular, it is not bijective (one-to-one). Before inverting, we must

**restrict**it to an interval where it is one-to-one. Most often, people choose [0, π] as the domain of this restricted cosine, and then this interval becomes the range of the inverse cosine.

## How to use this cos-1 calculator?

Our cos-1 calculator is very easy to operate! You **enter the argument x**, and the value of

`cos-1(x)`

appears in the blink of an eye. But please remember that you must not enter values that are not **between -1 and 1**!

Have you noticed our tool ***converts between radians and degrees?**. No need to search for any additional tools!

Happy with the cos-1 calculator? Omni features a whole collection of tools dealing with inverse trigonometric functions:

### Is the inverse cosine function antisymmetric?

**No**, the inverse cosine function is not antisymmetric. Note, for instance, that `cos-1(1) = 0`

and `cos-1(-1) = π`

; that is, `cos-1(1)`

and `cos-1(-1)`

are not opposite numbers. The inverse **sine** function, on the other hand, is antisymmetric, i.e., it satisfies `sin-1(-x) = -sin-1(x)`

.

### How do I calculate cos-1 of one half?

To determine the inverse cosine of ½:

- Sketch a
**right-angled triangle**. - Recall that the cosine is equal to the
**ratio**of the adjacent side to the hypotenuse. - So we need to determine an angle suc that the
**hypotenuse is twice as long as the adjacent side**. - Dig into your memory and recall that this angle must be equal to
**60°**. - If your memory no longer retains any stuff taught in geometry class, we recommend using an online cos inverse calculator ;)