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A-LevelMathematicsTrigonometry9709/12 · May/June 2020 · Q25 Marks

The following parts relate to trigonometric equations.

  1. (a)Express the equation 3 cos θ = 8 tan θ as a quadratic equation in sin θ.[3]
  2. (b)Hence find the acute angle, in degrees, for which 3 cos θ = 8 tan θ.[2]

Mark scheme

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

  1. [M1] 3 cos θ = 8 sin θ / cos θ
  2. [M1] 3(1 - sin²θ) = 8 sin θ
  3. [A1] 3 sin²θ + 8 sin θ - 3 = 0
  4. [M1] (3 sin θ - 1)(sin θ + 3) = 0 → sin θ = 1/3
  5. [A1] θ = 19.5°

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About this question

Topic
Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, May/June 2020 Paper 1 Variant 2, question 2.

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