The Unit Circle

Example of A Point on the Unit Circle

Terminal Points on the Unit Circle

Suppose t is a real number. If t >= 0, let’s mark off a distance t along the unit circle, starting at the point 11, 02 and moving in a counterclockwise direction. If t < 0, we mark off a distance 0 t 0 in a clockwise direction (Figure). In this way we arrive at a point P1x, y2 on the unit circle. The point P1x, y2 obtained in this way is called the terminal point determined by the real number t.

The circumference of the unit circle is C = 2p(1) = 2p. So if a point starts at (1, 0) and moves counterclockwise all the way around the unit circle and returns to (1, 0) , it travels a distance of 2p. To move halfway around the circle, it travels a distance of 1/2( 2p) = p. To move a quarter of the distance around the circle, it travels a distance of 1/4 (2p) = p/2. Where does the point end up when it travels these distances along the circle? From Figure 3 we see, for example, that when it travels a distance of p starting at (1, 0) , its terminal point is (-1, 0) .

Finding Terminal Points

The Reference Number

Finding Reference Numbers