Double- and Half-Angle Identities Worksheets
Practice exact trigonometric values and identities with angle units and domains stated.
Before you begin
Use radians, the unit circle and exact special-angle values.
Worked example
θ is in the first quadrant, with sin θ = 10/26 and cos θ = 24/26. Find sin(2θ).
- Use sin(2θ) = 2 sin θ cos θ.
Answer: 120/169
Check your result using the method in the example before moving to the next question.
Choose your level
These sets use the same exercise types and number ranges across level labels. Choose a fresh set for additional practice.
- Easy: Start with the preview and follow the worked example.
- Medium: Practice the same exercise types with a fresh numbered set.
- Hard: Use another set to practice explaining and checking your answers.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
θ is in the first quadrant, with sin θ = 6/10 and cos θ = 8/10. Find sin(2θ).
2
0 < θ < π and cos θ = 24/26. Find sin(θ/2) exactly.
3
θ is in the first quadrant, with sin θ = 8/17 and cos θ = 15/17. Find sin(2θ).
4
0 < θ < π and cos θ = 15/17. Find sin(θ/2) exactly.
5
θ is in the first quadrant, with sin θ = 12/37 and cos θ = 35/37. Find sin(2θ).
6
0 < θ < π and cos θ = 35/37. Find sin(θ/2) exactly.
Answer Key
1. 24/252. √(1/26)3. 240/2894. √(1/17)5. 840/13696. √(1/37)