Maths Extension 1 Year 11 - Module 3 - Lesson 10
Solving Trigonometric Equations, Linear
Name
Date
Class
1. Lesson focus
Solving linear trigonometric equations. Find reference angles, then include every solution in the stated interval; use the sign pattern of the function.
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 2cosx=−1 for 0≤x<2π.
3. Solve √3 tanx=3 for 0≤x<2π.
3. Challenge
Solve 2sinx−√3=0 on 0≤x<2π.
4. Multiple choice
Which are the solutions of cosx=−1/2 on 0≤x<2π?
A. π/3 and 5π/3
B. 2π/3 and 4π/3
C. π/6 and 5π/6
D. 0 and π
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. Solve 2sinx=1 for 0≤x<2π.
sinx=1/2 in quadrants I and II: x=π/6,5π/6.
2. Solve 2cosx=−1 for 0≤x<2π.
cosx=−1/2 in quadrants II and III: x=2π/3,4π/3.
3. Solve √3 tanx=3 for 0≤x<2π.
tanx=√3; reference angle π/3 and tangent is positive in I,III: x=π/3,4π/3.
Challenge. Solve 2sinx−√3=0 on 0≤x<2π.
sinx=√3/2 in quadrants I,II: x=π/3,2π/3.
Multiple choice. Which are the solutions of cosx=−1/2 on 0≤x<2π?
Correct answer: B. Cosine is negative in quadrants II and III, each with reference angle π/3.
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