O-LevelAdditional MathematicsTrigonometry4037/21 · Oct/Nov 2011 · Q35 Marks

Without using a calculator, find the value of cosθ, giving your answer in the form (a+b√3)/c where a, b and c are integers. [Figure: A triangle with side lengths 3, 2, and 2+√3. The angle θ is opposite the side of length 2+√3.]

Without using a calculator, find the value of cosθ, giving your answer in the form (a+b√3)/c where a, b and c are integers.[5]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.

[1] cos θ = (4+2+√3-9) / (4(2+√3)) or 9 = 4+(2+√3)²-4(2+√3)cosθ
[1] (2+√3)² = 7+4√3
[1] (2+4√3) / (4(2+√3))
[1] Multiply top and bottom by 2 – √3
[1] (-4+3√3)/2 oe

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Topic: Trigonometry, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2011 Paper 2 Variant 1, question 3.

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