# Unit Circle - Exact Values of Trigonometric Ratios

- Author:
- John Sweeney

- Topic:
- Circle, Ratios, Unit Circle

A

**unit circle**, a circle of radius 1 centered at the Origin, contains many patterns involving coordinates of points on the circle, as well as central angles of the circle. Drag the blue dot around the green unit circle to help you discover some of these patterns. Then answer the questions below.**Questions.**(1) What relationship(s) do you see between the coordinates of a point on the circle and the trigonometric ratios of the central angle? (2) What relationship(s) do you see between the signs of the coordinates of each of the points on the unit circle? (3) What relationship(s) do you see between the coordinates of a point on the unit circle and the coordinates of a point π radians from that point? (4) What other relationship(s) do you see?