Maths Extension 1 Year 11 - Module 3 - Lesson 5

Compound Angle Formulas

Use this worksheet after reading the lesson to practise the key ideas and prove you can meet the success criteria.

Name
Date
Class

1. Lesson focus

Compound-angle formulae. Use sin(A±B)=sinAcosB±cosAsinB and cos(A±B)=cosAcosB∓sinAsinB with exact special-angle values.

Success criteria

  • Apply the lesson method accurately in a routine example.
  • Show each algebraic or domain step and check the result.
  • Explain why the method and restrictions fit the question.

2. Worked practice

1. Find sin 75° exactly.

2. Find cos 75° exactly.

3. Find tan 75° exactly.

3. Challenge

Evaluate sin75°·cos15° exactly.

4. Multiple choice

What is cos(A+B)?

A. cosAcosB−sinAsinB

B. cosAcosB+sinAsinB

C. sinAcosB+cosAsinB

D. sinAcosB−cosAsinB

Worked answer key

Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.

1. Find sin 75° exactly.

sin(45°+30°)=(√6+√2)/4.

2. Find cos 75° exactly.

cos(45°+30°)=(√6−√2)/4.

3. Find tan 75° exactly.

tan(45°+30°)=(1+1/√3)/(1−1/√3)=2+√3.

Challenge. Evaluate sin75°·cos15° exactly.

cos15°=sin75°, so the product=sin²75°=(1−cos150°)/2=(2+√3)/4.

Multiple choice. What is cos(A+B)?

Correct answer: A. The cosine addition identity uses a minus between the cosine-cosine and sine-sine products.

HSCScience - Printable lesson worksheet - Maths Extension 1 Year 11 - Module 3 - Lesson 5

Want help with Worksheet - Compound Angle Formulas?

Tell us what you would like help with. Register interest; support details will be confirmed before enrolment.

Register interest →