The Cosine Function

Let P be the point of intersection of the unit circle and terminal side of an angle in standard position. The cosine function, denoted as cos, can be defined as the x-coordinate of the point P.

The graph of the cosine function looks as follows.

Note that for x in the interval [- 2π,0] and in the interval [0,2π] the graph looks exactly the same. This means that the cosine function is a periodic function and its period is 2π.

Here, n is any integer number. Consider the function y=acosbθ, where a and b are non-zero real numbers and θ is measured in radians. With this information, the properties of the cosine function can be defined.