Unit Circle Exploration
- Jan Mays
This construction is called the Unit Circle because the radius of the circle is 1 and its center is the origin. Recall that in a right triangle, the sine of an angle is the length of the side opposite the angle divided by the length of the hypotenuse. The cosine of an angle is the length of the side adjacent to the angle divided by the length of the hypotenuse. Drag point C around the circle to see the lengths that are used to calculate the sine and cosine. Point E has as its x-coordinate the length of the arc BC and its y-coordinate the length of CD. In the algebra window, click on the dot beside point E to show E and drag point C around the circle. What familiar function is traced out? Hide E (by clicking on the dot again) and show point F. Drag point C to trace out a new function. What should be the coordinates of point F?