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WMA12/01 Oct 2021, Question 10: Harder Trig Equations

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 10 marks

The question, in short

Solve two trigonometric equations, showing full working without relying on calculator methods: one in x over −π/2 < x < π/2, one in θ over 0 < θ < 360°.

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

Part (i) · 5 marks

Solve tan²(2x + π/4) = 3 for x in the interval −π/2 < x < π/2, showing all working.

  1. 1tan(2x + π/4) = ±√3
  2. 2−3π/4 < 2x + π/4 < 5π/4
  3. 32x + π/4 = −2π/3, −π/3, π/3, 2π/3
  4. 42x = −11π/12, −7π/12, π/12, 5π/12
  5. 5x = −11π/24, −7π/24, π/24, 5π/24

Answerx = −11π/24, −7π/24, π/24, 5π/24

Part (ii) · 5 marks

Solve (2 sin θ − cos θ)² = 1 for 0 < θ < 360°, giving answers to one decimal place where appropriate.

  1. 14sin²θ − 4 sin θ cos θ + cos²θ = 1
  2. 2Replace 1 with sin²θ + cos²θ: 3sin²θ − 4 sin θ cos θ = 0
  3. 3sin θ(3 sin θ − 4 cos θ) = 0
  4. 4sin θ = 0 ⇒ θ = 180° (0° and 360° are outside the range)
  5. 5tan θ = 4/3 ⇒ θ = 53.1°, 233.1°

Answerθ = 53.1°, 180°, 233.1°

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