A-LevelMathematicsTrigonometry9709/31 · May/June 2020 · Q36 Marks
Express the equation tan(θ+ 60°) = 2 + tan(60° – θ) as a quadratic equation in tan θ, and hence solve the equation for 0° ≤ θ ≤ 180°.
- (a)Express the equation tan(θ+ 60°) = 2 + tan(60° – θ) as a quadratic equation in tan θ, and hence solve the equation for 0° ≤ θ ≤ 180°.[6]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [M1] Use tan (A + B) formula and obtain an equation in tan θ
- [A1] Using tan 60° = √3, obtain a horizontal equation in tan θ in any correct form
- [A1] Reduce the equation to 3 tan² θ + 4 tan θ – 1 = 0, or equivalent
- [M1] Solve a 3-term quadratic for tan θ
- [A1] Obtain a correct answer, e.g. 12.1°
- [A1] Obtain a second correct answer, e.g. 122.9°, and no others in the given interval
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