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A-LevelMathematicsTrigonometry9709/22 · May/June 2021 · Q36 Marks

Solve the equation sin(2θ + 30°) = 5 cos(2θ + 60°) for 0° < θ < 180°.

  1. Solve the equation sin(2θ + 30°) = 5 cos(2θ + 60°) for 0° < θ < 180°.[6]

Mark scheme

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

  1. [B1] Expand at least one of sin(20+30) and cos(20+60) correctly
  2. [*M1] Attempt expansions and division by cos 20 to obtain equation in tan 20 only
  3. [A1] Obtain tan 2θ = - (4/(6√3)) or - (2/(3√3)) or - (2√3/9) or -0.3849...
  4. [A1] Obtain θ=10.5
  5. [DM1] Use correct process to find second value of θ
  6. [A1 FT] Obtain θ=100.5

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About this question

Topic
Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, May/June 2021 Paper 2 Variant 2, question 3.

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