Imagine the terminal side of an angle [math]\theta[/math] in standard position rotating smoothly around the Unit Circle. As [math]\theta[/math] changes, so do the values of [math]sin(\theta)[/math] (the y-value on the circle) and [math]cos(\theta)[/math] (the x-value). The values of these two functions change from 0 to 1 back to 0 to -1 and back to zero as the angle rotates around the Unit Circle.[br][br]If we plot the values of the functions as [math]\theta[/math] changes, we see the graphs of the sine and cosine functions.

Check or clear the checkboxes to show or hide either or both function graphs. You can drag the [math]\theta[/math] slider manually, or you can click the "PLAY" button at the lower left of the app to rotate [math]\theta[/math] automatically. At each value of [math]\theta[/math], the angle's terminal side intersects the unit circle at some (x, y) coordinate. These coordinates correspond to [math]x=cos(\theta)[/math] and [math]y=sin(\theta)[/math], as illustrated by the point on the graphs at the right.[br][br]Make the connection between y (red) on the unit circle and [math]sin(\theta)[/math] (red) on the graph by hiding the cosine graph, then switch. Observe especially what happens on the graph when [math]\theta[/math] is on the x- or y-axis.