[color=#9900ff]Follow the steps below to investigate a special relationship between the sine and cosine of complementary angles. You may work with a partner. [/color]
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)?
They are the same ratios. The sides have switched in the triangle when you switch reference angles.
DRAG Point B to enlarge/shrink the triangle. What do you notice about the sine and cosine of the two different angles?
1. Uncheck all boxes. [br]2. Click on cos(theta).[br]3. Click on complementary angle, then click on sin(90-theta).[br]4. Does the relationship still hold true?[br]5. Why do you think this is?