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O-Level Differentiation and integration: worked solution
3 marks. Full working, one step per line.
Question
With A = (1/4)x²(sin2θ + 2cosθ) and θ free to vary, find the value of θ that makes A stationary.
Worked answer
A = (1/4)x²(sin2θ + 2cosθ), with x constant. dA/dθ = (1/4)x²(2cos2θ - 2sinθ). Stationary: 2cos2θ - 2sinθ = 0, so cos2θ = sinθ. Using cos2θ = 1 - 2sin²θ: 1 - 2sin²θ = sinθ 2sin²θ + sinθ - 1 = 0 (2sinθ - 1)(sinθ + 1) = 0 sinθ = 1/2 or sinθ = -1 (rejected for an acute angle here). sinθ = 1/2 gives θ = π/6 (30°).
Practise this topic
This question is part of O-Level Differentiation and integration, in O-Level Additional Maths (A-Maths).
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