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WMA12/01 Jan 2020, Question 7: Solving Trig Equations

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 7 marks

The question, in short

Show that 8 tan θ = 3 cos θ rearranges to 3 sin²θ + 8 sin θ − 3 = 0, then use this to solve 8 tan 2x = 3 cos 2x for 0 ≤ x ≤ 90°, answers to 2 decimal places.

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

Part (a) · 3 marks

Show that 8 tan θ = 3 cos θ can be rewritten as 3 sin²θ + 8 sin θ − 3 = 0.

  1. 18 sin θ / cos θ = 3 cos θ
  2. 28 sin θ = 3 cos²θ
  3. 38 sin θ = 3(1 − sin²θ)
  4. 43 sin²θ + 8 sin θ − 3 = 0

AnswerShown: 8 sin θ = 3(1 − sin²θ) ⇒ 3 sin²θ + 8 sin θ − 3 = 0

Part (b) · 4 marks

Hence solve 8 tan 2x = 3 cos 2x for 0 ≤ x ≤ 90°, giving answers to 2 decimal places.

  1. 1From (a) with θ = 2x: 3 sin²2x + 8 sin 2x − 3 = 0
  2. 2(3 sin 2x − 1)(sin 2x + 3) = 0
  3. 3sin 2x = 1/3 (sin 2x = −3 has no solution)
  4. 42x = 19.47° or 180° − 19.47° = 160.53°
  5. 5x = 9.74° or 80.26°

Answerx = 9.74°, 80.26°

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