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U6 L2: Sine and Cosine of Complementary angles

Author:Laina Beale, 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?

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

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

Select all that apply
  • A
  • B
  • C
Check my answer (3)
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?

Select all that apply
  • A
  • B
  • C
Check my answer (3)
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)?

Check my answer

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?

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