Double and Half Angle Identities Worksheet

Double and Half Angle Identities

Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. If sin θ = 3/5 and θ is in the first quadrant, find the exact value of sin(2θ).

2. Given cos θ = -5/13 and θ is in the second quadrant, find the exact value of cos(2θ).

3. The double angle identity for tan(2θ) is tan(2θ) =  .

4. If cos(2θ) = 1 - 2sin²θ, then sin²θ =  .

5. If cos θ = 1/2 and θ is in the first quadrant, find the exact value of cos(θ/2).

6. Given sin θ = -√3/2 and θ is in the third quadrant, find the exact value of sin(θ/2).

7. The identity sin(2θ) = 2sinθcosθ is always true for all values of θ.

8. The half-angle formula for tan(θ/2) always results in a positive value.

9. Which of the following is an equivalent expression for cos(2θ)?

10. The sign of √( (1 - cos θ) / 2 ) for sin(θ/2) depends on the quadrant of:

11. Prove the identity: (sin 2θ) / (1 + cos 2θ) = tan θ