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4PM1/02R Jun 2022, Question 7: Solving Trig Equations

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 12 marks

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The question, in short

Solve three trigonometric equations in given degree intervals, giving answers to one decimal place where appropriate.

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

Part (a) · 4 marks

Solve cos(3x − 15)° = √3/2 for 0 ≤ x < 180.

  1. 13x − 15 = 30, 330 or 390
  2. 23x = 45, 345 or 405
  3. 3x = 15, 115, 135

Answerx = 15, 115, 135

Part (b) · 4 marks

Solve 3 tan y° + 4 sin y° = 0 for −180 ≤ y < 180.

  1. 13 sin y/cos y + 4 sin y = 0
  2. 2sin y(3/cos y + 4) = 0
  3. 3sin y = 0: y = −180, 0
  4. 4cos y = −3/4: y = ±138.6

Answery = −180, 0, 138.6, −138.6

Part (c) · 4 marks

Solve cos θ° = 3 sin²θ° − 1 for −180 ≤ θ < 180.

  1. 1cos θ = 3(1 − cos²θ) − 1
  2. 23cos²θ + cos θ − 2 = 0
  3. 3(3cos θ − 2)(cos θ + 1) = 0
  4. 4cos θ = 2/3: θ = ±48.2
  5. 5cos θ = −1: θ = −180

Answerθ = −180, 48.2, −48.2

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