The Unit Circle and Trigonometric Functions

The purpose of this applet is to illustrate the relation between the unit circle and how the trigonometric functions are defined. Use it as follows:

Drag the point around the unit circle, clockwise or counterclockwise, as many times as you want. As you do so, the following should happen:

  1. The coordinates of the point will be updated.
  2. The point will be in green if it corresponds to a positive angle, otherwise it will be red.
  3. Depending on which trigonometric function you have chosen (sine or cosine), its graph will appear and the point on the unit circle will also appear on the graph of the trigonometric function.
  4. A red line whose length is the value of the chosen trigonometric function will be displayed on both the unit circle and the graph.
  5. If the box "Show Function Values" is checked, the the angle and the value of the chosen trigonometric function at that angle will be displayed.
  6. As the point on the graph gets ready to leave the graph, the graph will scroll left or right, so that the point remains visible.