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A-LevelMathematicsTrigonometry9709/31 · Oct/Nov 2021 · Q25 Marks

Express 5 sin x – 3 cos x in the form Rsin(x – α), where R > 0 and 0 < α < ½π. Give the exact value of R and give α correct to 2 decimal places.

  1. (a)Express 5 sin x – 3 cos x in the form Rsin(x – α), where R > 0 and 0 < α < ½π. Give the exact value of R and give α correct to 2 decimal places.[3]
  2. (b)Hence state the greatest and least possible values of (5 sinx – 3 cos x)².[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

  1. [B1] State R = √34
  2. [M1] Use trig formulae to find α
  3. [A1] Obtain α = 0.54
  4. [B1 FT] State greatest value 34
  5. [B1] State least value 0

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About this question

Topic
Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Oct/Nov 2021 Paper 3 Variant 1, question 2.

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