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A-LevelMathematicsTrigonometry9709/22 · Feb/Mar 2020 · Q14 Marks

Solve the equation 2 sin(θ + 30°) + 5 cos θ = 2 sin θ for 0° < θ < 90°.

  1. Solve the equation 2 sin(θ + 30°) + 5 cos θ = 2 sin θ for 0° < θ < 90°.[4]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.

  1. Express first term as 2sinθcos30+2cosθsin30
  2. Divide by cosθ to produce linear equation in tanθ
  3. Obtain tanθ = 6/(2-√3) or 22.39...
  4. Obtain 87.4 Or greater accuracy 87.44297...

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About this question

Topic
Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source
A-Level Mathematics, Feb/Mar 2020 Paper 2 Variant 2, question 1.

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