WMA12/01 Jun 2022, Question 5: Harder Trig Equations
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 6 marks
The question, in short
Solve 3 tan(θ + 43°) = 2 cos(θ + 43°) for −180° < θ ≤ 180°, showing full working without relying on calculator-only methods.
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Solution · 6 marks
- 1Write tan as sin/cos: 3 sin(θ + 43°)/cos(θ + 43°) = 2 cos(θ + 43°)
- 23 sin(θ + 43°) = 2 cos²(θ + 43°) = 2(1 − sin²(θ + 43°))
- 32 sin²(θ + 43°) + 3 sin(θ + 43°) − 2 = 0
- 4(2 sin(θ + 43°) − 1)(sin(θ + 43°) + 2) = 0, and sin(θ + 43°) = −2 is impossible
- 5sin(θ + 43°) = 1/2, with −137° < θ + 43° ≤ 223°
- 6θ + 43° = 30° or 150°, so θ = −13° or 107°
Answerθ = −13°, θ = 107°
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