Maths Extension 1 Year 11 - Module 3 - Lesson 1

Introduction to Further Trigonometry

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

Unit-circle exact values and radians. Convert degrees with θ°×π/180; use the reference angle and quadrant for signs.

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. Convert 150° to radians.

2. Find sin(5π/6) and cos(5π/6).

3. Solve sin x=√3/2 for 0≤x<2π.

3. Challenge

Evaluate tan(5π/6) exactly and justify its sign.

4. Multiple choice

Which is cos(7π/6)?

A. −√3/2

B. √3/2

C. −1/2

D. 1/2

Worked answer key

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

1. Convert 150° to radians.

150π/180 = 5π/6.

2. Find sin(5π/6) and cos(5π/6).

Reference angle π/6 in QII: sin=1/2, cos=−√3/2.

3. Solve sin x=√3/2 for 0≤x<2π.

Reference angle π/3; sine is positive in I and II, so x=π/3, 2π/3.

Challenge. Evaluate tan(5π/6) exactly and justify its sign.

tan=sin/cos=(1/2)/(−√3/2)=−1/√3=−√3/3; tangent is negative in QII.

Multiple choice. Which is cos(7π/6)?

Correct answer: A. 7π/6 is in QIII with reference angle π/6; cosine is negative, so cos(7π/6)=−√3/2.

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

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