# Unit Circle: Complementary Angles

- Author:
- Brian Sterr

- Topic:
- Angles, Circle, Unit Circle

This sketch shows the relationship between an angle and its complement, . Drag around the circle and notice what happens to . How are the trigonometric ratios of the angles related?

## 1.

What is the geometric relationship between and ?

## 2.

The coordinates of are . From the relationship described in question 1, what are the coordinates of ?

## 3.

Since is a point on the unit circle corresponding to the angle in standard position, it has coordinates:

Therefore, for any angle , we have: