# Arccos Calculator (Inverse Cosine)

**Degrees:**

**Radians:**

**π radians:**

The domain considered is **-1 ≤ x ≤ 1**.

The range considered is **0 ≤ y ≤ π**.

This calculator allows you to determine the inverse cosine of an entered value. The answer will be displayed in degrees, radians, and π radians, only considering the range 0 ≤ y ≤ π.

Below you will find additional information on using the arccos calculator. In addition, you can also learn about the definition of inverse cosine, its graph, and some important values.

## How to use the inverse cosine calculator?

**Step 1:** Enter the value of *x* in the corresponding input box. The entered value must be in the domain **-1 ≤ x ≤ 1**.

** Step 2:** The corresponding angle in degrees will be displayed in the right panel.

** Step 3:** The boxes at the bottom will show the angle in radians and π radians.

## Difference between results in degrees, radians, and π radians

One complete revolution of a circle is equal to 360° or 2π radians. This means that 180° is equal to π radians.

The difference between π radians and radians is simply that the result in “radians” is already multiplied by π, while in “π radians” it is not. For example, the result 1.5 π radians is equal to 4.712, since π has a value of approximately 3.1415…

## What is inverse cosine?

The inverse cosine, also called the arc cosine and denoted cos^{-1}(x) or also arccos(x), is the inverse cosine function. This means that the inverse cosine reverses the effects of the cosine function.

For example, the cosine of 60° is equal to 0.5. This means that the inverse cosine of 0.5 is equal to 60°.

Inverse cosine can be used when we want to find an angle, and we have the proportions of the sides of a triangle. For example, we can find angle A in the following triangle using arccos(x), where *x* equals *b*/*c*.

## Why does the inverse cosine function only accept values from -1 to 1?

The inverse cosine function has a domain from -1 to 1 because it is the inverse cosine function. This means that the domain and range are swapped.

Considering the cosine function, there is no angle that we can use to get a value greater than 1 or less than -1. Cosine output values are always between -1 and 1, therefore inverse cosine input values must also be between those values.

## Graph of inverse cosine

The arc cosine function can be graphed by considering specific intervals for the input and output values. In the inverse cosine used in this calculator, the x values range from -1 to 1 and the output or y values range from 0 to π.

### Inverse cosine domain

Using the graph, we can see that the domain of the function, that is, the values of *x*, range from -1 to 1. Therefore, the domain is **-1 ≤ x ≤ 1**.

### Inverse cosine range

In the graph, we can see that the function has a range from 0 to π. Therefore, its range is **0 ≤ y ≤ π**.

## Table of inverse cosines of common values

Value of x | arccos(x)(rad) | arccos(x)(°) |
---|---|---|

-1 | π | 180° |

-√3/2 | 5π/6 | 150° |

-√2/2 | 3π/4 | 135° |

-1/2 | 2π/3 | 120° |

0 | π/2 | 90° |

1/2 | π/3 | 60° |

√2/2 | π/4 | 45° |

√3/2 | π/6 | 30° |

1 | 0 | 0° |

## Related calculators:

- Arcsin Calculator (Inverse Sine) – Degrees and Radians
- Arctan Calculator (Inverse Tangent) – Degrees and Radians
- Arcsec Calculator (Inverse Secant) – Degrees and Radians
- Arccsc Calculator (Inverse Cosecant) – Degrees and Radians
- Arccot Calculator (Inverse Cotangent) – Degrees and Radians

You can explore other calculators here.