U6 L2: Sine and Cosine of Complementary angles
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?