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

Arccosine formula

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

Composition of arccosine and cosine

Properties of Arccosine

Arccosine Table

The arccosine of the most common values is:

Table of the arccosine of the most characteristic angles (0º, 30º, 45º, 60º, 90º, 180º and 270º)

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:

Graph of the cosine function in arccosine 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).

Graph of the arccosine function

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).

Graph of the cosine and arccosine functions, being symmetric with respect to the line 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.

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