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Double & Half Angle Identities - Worksheet 5 - 12th Grade

Medium

Apply double-angle and half-angle formulas (Medium)

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

About This Worksheet

This medium-level worksheet contains 18 problems designed for 12th Grade students practicing double & half angle identities. Medium worksheets introduce larger numbers and varied question formats to deepen understanding and build fluency.

Double and half-angle formulas are essential tools in calculus — they appear in the integration of trigonometric powers, in the derivation of the derivative of sine, and in physics applications involving wave superposition. Fluency with these identities significantly reduces the difficulty of calculus integration problems.

  • Apply double-angle formulas for sine and cosine
  • Derive and apply the half-angle formulas for sine and cosine
  • Use double and half-angle formulas to evaluate trig functions at non-standard angles and to prove identities
  • Simplify trig expressions using the three forms of the double-angle cosine formula
  • Determine the correct sign when applying the half-angle formula from the quadrant

How to Solve: Worked Example

Example Problem: Solve the first problem on the worksheet.
Solution Steps:
  1. Read the problem carefully.
  2. Identify what is being asked.
  3. Use what you know to find the answer.
  4. Check your work.
Answer: See the answer key below
Tip: Take your time and read each problem carefully before answering!
1
9 + 6 =
2
3 + 5 =
3
3 + 2 =
4
6 + 1 =
5
7 + 3 =
6
4 + 6 =
7
1 + 3 =
8
5 + 8 =
9
9 + 4 =
10
6 + 5 =
11
2 + 10 =
12
2 + 6 =
13
7 + 5 =
14
1 + 7 =
15
3 + 6 =
16
10 + 3 =
17
5 + 2 =
18
4 + 1 =

Answer Key

1. 152. 83. 54. 75. 106. 107. 48. 139. 1310. 1111. 1212. 813. 1214. 815. 916. 1317. 718. 5

Frequently Asked Questions

How do I download this double & half angle identities - worksheet 5 worksheet?

Click the "Download PDF / Print" button at the top of the worksheet. You can save it as a PDF or print it directly. The answer key will be on a separate page.

How do I find worksheets at different difficulty levels?

Each subtopic has 10 worksheets: Worksheets 1-3 are Easy, 4-7 are Medium, and 8-10 are Hard. Start with Easy worksheets to build confidence, then progress to harder ones.

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.

Can I use this worksheet in my classroom?

Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.

How many problems are on this worksheet?

This worksheet contains 18 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.