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A-LevelMathematicsTrigonometry9709/12 · May/June 2014 · Q35 Marks

The reflex angle θ is such that cos θ = k, where 0 < k < 1.

  1. (i)(a)Find an expression, in terms of k, for sin θ,[2]
  2. (i)(b)Find an expression, in terms of k, for tan θ.[1]
  3. (ii)Explain why sin 2θ is negative for 0 < k < 1.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.

  1. [B1 B1] sin θ = –√(1-k²) B1 rest B1
  2. [B1] Uses t=s/c → –√(1-k²)/k √ for (i) ÷ k.
  3. [B1] θ is in 4th quadrant. co
  4. [B1] 2θ lies between 540° and 720° sin2θ is negative in both these quadrants. co

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About this question

Topic
Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, May/June 2014 Paper 1 Variant 2, question 3.

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