A-LevelMathematicsTrigonometry9709/32 · May/June 2017 · Q35 Marks
Express the equation cot θ – 2 tan θ = sin 2θ in the form a cos⁴ θ + b cos² θ + c = 0, where a, b and c are constants to be determined.
- (i)Express the equation cot θ – 2 tan θ = sin 2θ in the form a cos⁴ θ + b cos² θ + c = 0, where a, b and c are constants to be determined.[3]
- (ii)Hence solve the equation cot θ – 2 tan θ = sin 2θ for 90° < θ < 180°.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [M1] Use correct formulae to express the equation in terms of cos θ and sin θ
- [M1] Use Pythagoras and express the equation in terms of cos θ only
- [A1] Obtain correct 3-term equation, e.g. 2cos⁴ θ + cos² θ – 2 = 0
- [M1] Solve a 3-term quadratic in cos² θ for cos θ
- [A1] Obtain answer θ = 152.1° only
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