Graphs of the Sine and Cosine Functions
- Ken Schwartz
Imagine the terminal side of an angle in standard position rotating smoothly around the Unit Circle. As changes, so do the values of (the y-value on the circle) and (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. If we plot the values of the functions as 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 slider manually, or you can click the "PLAY" button at the lower left of the app to rotate automatically. At each value of , the angle's terminal side intersects the unit circle at some (x, y) coordinate. These coordinates correspond to and , as illustrated by the point on the graphs at the right. Make the connection between y (red) on the unit circle and (red) on the graph by hiding the cosine graph, then switch. Observe especially what happens on the graph when is on the x- or y-axis.