is the side of the triangle that is part of angle , and is the side opposite the right angle.
The cosine of an angle is the x-coordinate of the point of intersection of said angle and a unit circle.
As a result of Euler's formula, the cosine function can also be represented as
The trigonometric addition/subtraction identiy of cosine is:
The square of cosine:
More formally defined, the cosine is defined by the power series, which is convergent for all ,
Where denotes the factorial of n. From this, the above properties may be derived.