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A-LevelMathematicsTrigonometry9709/22 · Feb/Mar 2023 · Q25 Marks

Solve the equation tan(θ – 60°) = 3 cot θ for −90° < θ < 90°.

  1. (a)Solve the equation tan(θ – 60°) = 3 cot θ for −90° < θ < 90°.[5]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2023). The mark or mark type is shown in brackets.

  1. [B1] State (tanθ - tan 60)/(1 + tanθ tan 60) = 3/tanθ OE involving tan only.
  2. [M1] Attempt arrangement of equation to quadratic form. Condone sign errors in first step and retention of tan 60.
  3. [A1] Obtain tan²θ-4√3 tanθ-3=0 OE involving decimals.
  4. [M1] Solve 3-term quadratic equation to obtain at least one value of θ
  5. [A1] Obtain -22.2 and 82.2 Or greater accuracy; and no others between –90 and 90.

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About this question

Topic
Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Feb/Mar 2023 Paper 2 Variant 2, question 2.

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