Double Angle Properties for Trigonometry

Use the rules above to solve the questions listed below. For the following exercises, do not solve for x but find the exact values of

1. sin(2𝑥)
2. cos(2x)
3. tan(2x)

5. If sin 𝑥 = 1/8, and 𝑥 is in quadrant I.

6. If cos 𝑥 = 2/3, and 𝑥 is in quadrant I.

7. If cos 𝑥 = −1/2, and 𝑥 is in quadrant III.

8. If tan 𝑥 = −8, and 𝑥 is in quadrant IV.

For the following exercises, find the values of  sin (2𝜃), cos (2𝜃), tan (2𝜃), cot (2𝜃), sec (2𝜃), csc (2𝜃) if the conditions provided hold.

9. cos (2𝜃) = 3/5 and 90° ≤ 𝜃 ≤ 180°

10. cos (2𝜃) = 1/2 and 180° ≤ 𝜃 ≤ 270°