This file can be used to show how the graph of y = sin(t) is generated. To do this, use the slider to change the values of t As you do so, notice that a point will move along the unit circle on the left. There will be a blue arc of length t and it will show the y-coordinate of the terminal point of that arc. At the same time, the point (t, y) will be plotted on the graph of y = sin(t) on the right.
This applet can be use to show how the graph of y = sin(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 = sin(t).
For each value of t, a point corresponding to the arc of length t is drawn on the unit circle. The y-coordinate of this point is sin(t) This is illustrated by the (signed) length of the red line segment from the horizontal axis to the point on the circle.
At the same time, a point on the graph of y = sin(t) is drawn. The point will have coordinates (t, sin(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.