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WMA12/01 Oct 2019, Question 9: Solving Trig Equations

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 12 marks

The question, in short

Solve a trigonometric equation in degrees to one decimal place, then work with three arithmetic sequence terms involving sin α and tan α to derive an identity and find α in radians.

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

Part (i) · 4 marks

Solve 3 sin(2θ − 10°) = 1 for 0 ≤ θ < 180°, giving answers to one decimal place.

  1. 1sin(2θ − 10°) = 1/3
  2. 22θ − 10° = 19.47° or 180° − 19.47° = 160.53°
  3. 32θ = 29.47° or 170.53°
  4. 4θ = 14.7° or 85.3°

Answerθ = 14.7°, 85.3°

Part (iia) · 3 marks

Show that 2 cos α = 3 sin² α using the three arithmetic sequence terms.

  1. 1Common difference: 1/tan α − sin α = 2 sin α − 1/tan α
  2. 22/tan α = 3 sin α
  3. 32 cos α / sin α = 3 sin α
  4. 42 cos α = 3 sin² α

AnswerShown: 1/tan α − sin α = 2 sin α − 1/tan α gives 2cos α/sin α = 3 sin α, so 2 cos α = 3 sin² α

Part (iib) · 5 marks

Given π < α < 2π, find α to 3 decimal places, showing all working.

  1. 12 cos α = 3(1 − cos² α)
  2. 23cos² α + 2cos α − 3 = 0
  3. 3cos α = (−2 ± √40)/6, so cos α = 0.7208 (the other root, −1.387, is impossible)
  4. 4arccos 0.7208 = 0.7669 radians
  5. 5In π < α < 2π: α = 2π − 0.7669 = 5.517

Answerα = 5.517

Stuck on a step? Read the free lesson: Solving Trig Equations

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