To graph the cosine function, we mark the angle along the horizontal x axis, and for each angle, we put the cosine of that angle on the vertical y-axis. The result, as seen below, is a smooth curve that varies from +1 to -1. It is the same shape as the sine function but displaced to the left 90°. The shape of the cosine curve is the same for each full rotation of the angle and so the function is called 'periodic'. The period of the function is 360° or `2 pi` radians.
Drag the red dot and see the values obtained by the cosine function. Check that the period of the cosine function is `2 pi`.
You know how to graph many types of functions. Graphs are useful because they can take complicated information and display it in a simple, easy-to-read manner. The graphs of trigonometric functions have several properties to elicit (Amplitude, Interval, Period, Horizontal Shift, Vertical Shift). To be able to graph these functions by hand, we have to understand them. Good calculators have sin, cos and tan on them, to make it easy for you. Just put in the angle and press the button. But you still need to remember what they mean!