WMA12/01 Oct 2024, Question 9: Solving Trig Equations
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 7 marks
The question, in short
Show detailed reasoning throughout, with calculator-only solutions unacceptable: transform a trigonometric equation into a quadratic in sin θ, then solve a related equation for x in a given interval.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 3 marks
Show that 2tan θ = 3cos θ rearranges to the quadratic 3sin²θ + 2sin θ − 3 = 0, with full working.
- 12sin θ / cos θ = 3cos θ
- 22sin θ = 3cos²θ
- 32sin θ = 3(1 − sin²θ)
- 43sin²θ + 2sin θ − 3 = 0
AnswerShown: 2sin θ = 3cos²θ = 3(1 − sin²θ), so 3sin²θ + 2sin θ − 3 = 0
Part (b) · 4 marks
Using part a, solve 2tan(2x + π/3) = 3cos(2x + π/3) for −π < x < π, giving answers to 3 significant figures.
- 1Let θ = 2x + π/3: 3sin²θ + 2sin θ − 3 = 0
- 2sin θ = (−1 ± √10)/3; (−1 − √10)/3 < −1 so only sin θ = (−1 + √10)/3 = 0.7207…
- 3θ = 0.8049… or π − 0.8049… = 2.3367…, plus or minus 2π, with −5π/3 < θ < 7π/3
- 40.8049 − 2π = −5.4783 is out of range, so θ = 2.3367 − 2π = −3.9465, 0.8049, 2.3367, 0.8049 + 2π = 7.0881
- 5x = (θ − π/3)/2 gives x = −2.50, −0.121, 0.645, 3.02
Answerx = −2.50, −0.121, 0.645, 3.02
Stuck on a step? Read the free lesson: Solving Trig Equations
Practise more solving trig equations questions
Real XMA01 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on solving trig equations
Also searched as: WMA12 October 2024 · WMA12/01 · wma12 oct24 · IAS Maths Pure Mathematics 2 October 2024 · question 9.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.