Double and Half Angle Identities Worksheet

Double and Half Angle Identities

Read each question carefully and provide your answers using the double and half-angle identities. Show all your work for full credit.

1. The double angle identity for sin(2θ) is  .

2. One form of the double angle identity for cos(2θ) is  .

3. The half angle identity for tan(θ/2) can be expressed as  .

4. If cos(θ) = 3/5 and θ is in Quadrant I, then sin(θ/2) =  .

1. Which of the following is equivalent to 2sin(x)cos(x)?

2. If tan(θ) = 1/2 and θ is in Quadrant I, what is the value of tan(2θ)?

1. Express sin(θ) in terms of cos(θ/2) using a half-angle identity.

2. Verify the identity: (sin(2x))/(1+cos(2x)) = tan(x).

1. The identity cos(2θ) = 1 - 2sin²(θ) is a double angle identity.

2. The half-angle identity for cos(θ/2) is always positive.

1. Given sin(θ) = 4/5 and θ is in Quadrant II, find the exact values of sin(2θ), cos(2θ), and tan(2θ).

2. Use half-angle identities to find the exact value of sin(22.5°).