### Home > PC > Chapter 6 > Lesson 6.3.2 > Problem6-130

6-130.

If sin x = −, x [π, ], find exact values for sin 2x and cos 2x. Homework Help ✎

Draw and label a circle with the reference angle in the correct quadrant.
Find the length of the unlabeled side.

Use the Double Angle Formula for the sine to find sin(2x).

Use one of the Double Angle Formulas for the cosine to find cos(2x).

Double - Angle Formulas: Sine
sin(2α) = 2sin(α)cos(α)

Double - Angle Formulas: Cosine
1. cos(2α) = 1 − 2sin2(α)
2. cos2(α) = 2cos2(α) − 1
3. cos(2α) = cos2(α) − sin2(α)