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WMA12/01 Jan 2023, Question 8: Harder Trig Equations

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 9 marks

The question, in short

Solve two trigonometric equations showing full working: one in radians with a sine function of 3x + 0.1, one in degrees involving tan θ and sin θ, giving answers to stated accuracy.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (i) · 4 marks

Solve 5 sin(3x + 0.1) + 2 = 0 for −π/2 < x < π, giving answers in radians to 2 decimal places.

  1. 1sin(3x + 0.1) = −2/5
  2. 2Range for 3x + 0.1: −4.61 < 3x + 0.1 < 9.52
  3. 3sin⁻¹(−0.4) = −0.4115
  4. 43x + 0.1 = −2.730, −0.4115, 3.553, 5.872
  5. 5x = (value − 0.1) ÷ 3
  6. 6x = −0.94, −0.17, 1.15, 1.92

Answerx = −0.94, −0.17, 1.15, 1.92

Part (ii) · 5 marks

Solve 2 tan θ sin θ = 5 + cos θ for 0 < θ < 360°, giving answers in degrees to one decimal place.

  1. 12 (sin θ/cos θ) sin θ = 5 + cos θ ⇒ 2sin²θ = 5cos θ + cos²θ
  2. 22(1 − cos²θ) = 5cos θ + cos²θ
  3. 33cos²θ + 5cos θ − 2 = 0
  4. 4(3cos θ − 1)(cos θ + 2) = 0 ⇒ cos θ = 1/3 (cos θ = −2 has no solution)
  5. 5θ = 70.5° or 360° − 70.5° = 289.5°

Answerθ = 70.5°, 289.5°

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