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Double & Half Angle Identities - Worksheet 8 - 12th Grade

Hard

Practice exact trigonometric values and identities with angle units and domains stated.

hard: Use another set to practice explaining and checking your answers.

23 problems · 25-30 minutes · Skills: trigonometry, identities, algebra

About This Worksheet

This hard-level worksheet contains 23 problems designed for 12th Grade students practicing double & half angle identities. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

Use radians, the unit circle and exact special-angle values.

  • Practice exact trigonometric values and identities with angle units and domains stated.
  • Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: θ is in the first quadrant, with sin θ = 10/26 and cos θ = 24/26. Find sin(2θ).
Solution Steps:
  1. Use sin(2θ) = 2 sin θ cos θ.
Answer: 120/169
Tip: Check your result using the method in the example before moving to the next question.
1
θ is in the first quadrant, with sin θ = 4/5 and cos θ = 3/5. Find sin(2θ).
2
0 < θ < π and cos θ = 35/37. Find sin(θ/2) exactly.
3
θ is in the first quadrant, with sin θ = 10/26 and cos θ = 24/26. Find sin(2θ).
4
0 < θ < π and cos θ = 3/5. Find sin(θ/2) exactly.
5
θ is in the first quadrant, with sin θ = 6/10 and cos θ = 8/10. Find sin(2θ).
6
0 < θ < π and cos θ = 15/17. Find sin(θ/2) exactly.
7
θ is in the first quadrant, with sin θ = 8/17 and cos θ = 15/17. Find sin(2θ).
8
0 < θ < π and cos θ = 24/26. Find sin(θ/2) exactly.
9
θ is in the first quadrant, with sin θ = 12/37 and cos θ = 35/37. Find sin(2θ).
10
0 < θ < π and cos θ = 8/10. Find sin(θ/2) exactly.
11
θ is in the first quadrant, with sin θ = 6/10 and cos θ = 8/10. Find sin(2θ).
12
0 < θ < π and cos θ = 15/17. Find sin(θ/2) exactly.
13
θ is in the first quadrant, with sin θ = 12/37 and cos θ = 35/37. Find sin(2θ).
14
0 < θ < π and cos θ = 35/37. Find sin(θ/2) exactly.
15
θ is in the first quadrant, with sin θ = 8/17 and cos θ = 15/17. Find sin(2θ).
16
0 < θ < π and cos θ = 8/10. Find sin(θ/2) exactly.
17
θ is in the first quadrant, with sin θ = 10/26 and cos θ = 24/26. Find sin(2θ).
18
0 < θ < π and cos θ = 15/17. Find sin(θ/2) exactly.
19
θ is in the first quadrant, with sin θ = 8/17 and cos θ = 15/17. Find sin(2θ).
20
0 < θ < π and cos θ = 3/5. Find sin(θ/2) exactly.
21
θ is in the first quadrant, with sin θ = 4/5 and cos θ = 3/5. Find sin(2θ).
22
0 < θ < π and cos θ = 35/37. Find sin(θ/2) exactly.
23
θ is in the first quadrant, with sin θ = 10/26 and cos θ = 24/26. Find sin(2θ).

Answer Key

1. 24/252. √(1/37)3. 120/1694. √(1/5)5. 24/256. √(1/17)7. 240/2898. √(1/26)9. 840/136910. √(1/10)11. 24/2512. √(1/17)13. 840/136914. √(1/37)15. 240/28916. √(1/10)17. 120/16918. √(1/17)19. 240/28920. √(1/5)21. 24/2522. √(1/37)23. 120/169

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What skills does this trigonometry & circular functions worksheet cover?

This worksheet focuses on trigonometry, identities, algebra. It is designed for 12th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

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How many problems are on this worksheet?

This worksheet contains 23 problems. It typically takes 25-30 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.