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WMA12/01 Jun 2021, Question 8: Solving Trig Equations

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

The question, in short

Solve a trig equation in degrees and reduce a cubic-sine identity to a quadratic in cos x, then find all roots in a given interval.

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

Part (i) · 4 marks

Find θ between 0 and 360° from a tangent ratio of 7/3, giving one decimal place.

  1. 1Divide by cos(θ + 30°): tan(θ + 30°) = 7/3
  2. 2θ + 30° = arctan(7/3) = 66.80°
  3. 3θ + 30° = 66.80° or 246.80°
  4. 4θ = 36.8° or 216.8°

Answerθ = 36.8° or θ = 216.8°

Part (iia) · 2 marks

Show the given sine-cosine equation rearranges to sin x times a quadratic in cos x, finding constants a, b, c.

  1. 13 sin x (1 − cos²x) = 5 sin x − 7 sin x cos x
  2. 2sin x (5 − 7cos x + 3cos²x − 3) = 0
  3. 3sin x (3cos²x − 7cos x + 2) = 0: a = 3, b = −7, c = 2

AnswerShown: sin x (3cos²x − 7cos x + 2) = 0, so a = 3, b = −7, c = 2

Part (iib) · 4 marks

Use the factorised form to solve for x in the interval −π/2 to π/2.

  1. 1sin x = 0 gives x = 0
  2. 23cos²x − 7cos x + 2 = (3cos x − 1)(cos x − 2) = 0
  3. 3cos x = 2 has no solutions
  4. 4cos x = 1/3 gives x = ±arccos(1/3) = ±1.23
  5. 5Solutions: x = −1.23, 0, 1.23

Answerx = 0, x = 1.23, x = −1.23 (radians)

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

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