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A-LevelMathematicsTrigonometry9709/32 · Feb/Mar 2019 · Q36 Marks

Given that sin(θ + 45°) + 2 cos(θ + 60°) = 3 cos θ, find the exact value of tan θ in a form involving surds. You need not simplify your answer.

  1. (i)Given that sin(θ + 45°) + 2 cos(θ + 60°) = 3 cos θ, find the exact value of tan θ in a form involving surds. You need not simplify your answer.[4]
  2. (ii)Hence solve the equation sin(θ + 45°) + 2 cos(θ + 60°) = 3 cos θ for 0° < θ < 360°.[2]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.

  1. [M1] Use trig formulae and obtain an equation in sin θ and cos θ
  2. [A1] Obtain a correct equation in any form
  3. [M1] Substitute exact trig ratios and obtain an expression for tan θ
  4. [A1] Obtain answer tan θ = (2√2-1) / (1-√6), or equivalent
  5. [B1] State answer, e.g. θ = 128.4°
  6. [B1ft] State second answer, e.g. θ = 308.4°

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About this question

Topic
Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, Feb/Mar 2019 Paper 3 Variant 2, question 3.

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