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A-LevelMathematicsTrigonometry9709/23 · May/June 2025 · Q711 Marks

Express 4 cosθsin(θ+30°) in the form Rcos(2θ-α)+k, where R > 0, 0° < α < 90° and k is a constant.

  1. (a)Express 4 cosθsin(θ+30°) in the form Rcos(2θ-α)+k, where R > 0, 0° < α < 90° and k is a constant.[6]
  2. (b)Hence solve the equation 12 cos 2φ sin (2φ+30°) = 5 for 0° < φ < 90°.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

  1. [M1] Expand to obtain the form k₁ cosθsinθ + k₂ cos² θ
  2. [A1] Obtain 2√3 cosθsinθ + 2cos² θ with exact coefficients
  3. [A1] Obtain √3sin 2θ + cos2θ + 1
  4. [B1] State R = 2
  5. [M1] Use appropriate trigonometry to find value of α
  6. [A1] Conclude 2cos(2θ-60°)+1
  7. [*M1] Attempt to express equation in form cos(4φ-a)=k
  8. [DM1] Use correct process to find one value of φ
  9. [A1] Obtain cos(4φ – 60) = 1/3 and hence 32.6
  10. [DM1] Use correct process to find second value of φ
  11. [A1] Obtain 87.4 and no others between 0 and 90

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About this question

Topic
Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 11 marks.
Source
A-Level Mathematics, May/June 2025 Paper 2 Variant 3, question 7.

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