# Arccosine

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The arccosine (notation: arccos or cos-1) is the inverse function of the cosine. That is:

As the arcsine and sine are inverse functions, their composition is the identity. That is:

## Arccosine Table

The arccosine of the most common values is:

## Graphical Representation of the Arccosine Function

To better understand the graph of the arccosine, let’s first see the graphical representation of the sine function:

As we see in the graph above the cosine is periodic, it is not one-to-one and the graph of the cosine function fails the horizontal line test. Hence the cosine does not have an inverse unless we restrict its domain. So, by convention, the domain of the cosine is usually restricted to the interval (0, π).

The graph of the arccosine function is symmetric to that of the cosine function to the bisector line of the first and third quadrants (y = x).

AUTHOR: Bernat Requena Serra

YEAR: 2021

### 2 Responses

1. Mohamed says:

Your graph shows the sine function, not the cosine. Please revise it for confusion.

• Bernat Requena Serra says:

Thank you Mohammed. We have corrected it.