The following applet allows you to explore the relationship between the Unit Circle and the function y=cos(x), where x is the angle graphed on the Unit Circle.
Change the angle by dragging the slider. If you want to see the relationship for a specific angle, type that angle in the input box.
Remember that cosine of any angle is equal to the x-coordinate of the point on the Unit Circle, shown by the red horizontal segment in the Unit Circle. Since that distance is then graphed vertically (as the output of the corresponding angle) it has been rotated 90 degrees to help you see the relationship.