Maths Extension 1 Year 11 - Module 3 - Lesson 12
Solving Trigonometric Equations, Multiple Angles
Name
Date
Class
1. Lesson focus
Multiple-angle equations. For sin(nx)=c or cos(nx)=c, solve for the compound angle nx first, then divide and enumerate every x in the interval.
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
2. Solve cos3x=1 for 0≤x<2π.
3. Solve sin2x=√3/2 for 0≤x<2π.
3. Challenge
Solve cos2x=−1 for 0≤x<2π.
4. Multiple choice
What is the spacing between consecutive zeros of sin(3x)?
A. 2π
B. 2π/3
C. π
D. π/3
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. Solve sin2x=0 for 0≤x<2π.
2x=kπ; x=kπ/2, giving 0,π/2,π,3π/2.
2. Solve cos3x=1 for 0≤x<2π.
3x=2kπ; x=2kπ/3, giving 0,2π/3,4π/3.
3. Solve sin2x=√3/2 for 0≤x<2π.
2x=π/3,2π/3,7π/3,8π/3; divide by 2: x=π/6,π/3,7π/6,4π/3.
Challenge. Solve cos2x=−1 for 0≤x<2π.
2x=π+2kπ; in the interval x=π/2,3π/2.
Multiple choice. What is the spacing between consecutive zeros of sin(3x)?
Correct answer: D. Sine repeats every 2π in its angle, so sin(3x) repeats every 2π/3; zeros themselves are spaced π/3 apart. The question asks the zero spacing, so π/3.
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