This applet can be use to show how the graph of y = cos(t) is constructed. The slider is used to change the value of the variable t . (The value of t can go from 0 to 7 in increments of 0.2.)
The unit circle has been moved to the left so it will not interfere with the graph of y = cos(t).
For each value of t, a point corresponding to the arc of length t is drawn on the unit circle. The x-coordinate of this point is cos(t) This is illustrated by the (signed) length of the red line segment from the vertical axis to the point on the circle.
At the same time, a point on the graph of y = cos(t) is drawn. The point will have coordinates (t, cos(t)) and the length of the red line segment drawn on this graph is equal to the length of the red line segment on the unit circle.

To run this applet again, use the "Refresh" command in the "View" menu.