# U6 L2: Sine and Cosine of Complementary angles

- Author:
- Laina Petkevicius, Susan Socha

## An Exploration of Sine and Cosine of complementary angles

## INVESTIGATE IT!

Follow the steps below to investigate a special relationship between the sine and cosine of complementary angles. You may work with a partner.

1. What is the complement of a 35 degree angle?

2. What is the sin(35) expressed as a ratio?

CLICK on the box for the sin(theta) does your ratio you picked above match the calculation for sin(theta)?

CLICK on complementary angle.

3. What is the cos(55) expressed as a ratio?

CLICK on the box for the cos(90-x) does your ratio you picked above match the calculation for cos(90-x)?

4. What do you notice about the sine of an angle and the cosine of its complement (complementary angle)?

## THINK:

DRAG Point B to enlarge/shrink the triangle. What do you notice about the sine and cosine of the two different angles?

## REFLECT:

1. Uncheck all boxes.
2. Click on cos(theta).
3. Click on complementary angle, then click on sin(90-theta).
4. Does the relationship still hold true?
5. Why do you think this is?