Cosine function, cos(x)

Cosine definition

In a right triangle ABC the sine of α, sin(α) is defined as the ratio betwween the side adjacent to angle α and the side opposite to the right angle (hypotenuse):

cos α = b / c

For example:

b = 5″
c = 10″
cos α = b / c = 5 / 10 = 0.5

Graph of cosine


Cosine rules

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Inverse cosine function

The arccosine of x is defined as the inverse cosine function of x when -1≤x≤1.

When the cosine of y is equal to x:


cos y = x

Then the arccosine of x is equal to the inverse cosine function of x, which is equal to y:

arccos x = cos-1 x = y

For example:

arccos 1 = cos-1 1 = 0 rad = 0°

Cosine table

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