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A-LevelMathematicsTrigonometry9709/33 · Oct/Nov 2021 · Q55 Marks

Solve the equation sin θ = 3 cos 2θ + 2, for 0° ≤ θ ≤ 360°.

  1. Solve the equation sin θ = 3 cos 2θ + 2, for 0° ≤ θ ≤ 360°.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

  1. [M1] Use double angle formula and obtain an equation in sin θ
  2. [A1] Reduce to 6sin²θ + sin θ − 5 = 0, or 3-term equivalent
  3. [M1] Solve a 3-term quadratic in sin θ and calculate θ
  4. [A1] Obtain answer, e.g. 56.4°
  5. [A1] Obtain second and third answers, e.g.123.6° and 270° and no others in the given interval

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About this question

Topic
Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Oct/Nov 2021 Paper 3 Variant 3, question 5.

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