To graph the sine function, we mark the angle along the horizontal x axis, and for each angle, we put the sine of that angle on the vertical y-axis. The result, as seen below, is a smooth curve that varies from +1 to -1. Curves that follow this shape are called 'sinusoidal' after the name of the sine function. This shape is also called a sine wave, especially when it appears in radio and electronic circuits.

Drag the red dot and see the values obtained by the sine function. Check that the period of the sine function is `2 pi`.

Created with GeoGebra by Vitor Nunes

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!