CAPE Pure Mathematics Unit 1 · May/June 2014 · Paper 2 · Question 3(b)(i)
Express f(θ) = 3 sin 2θ + 4 cos 2θ in the form r sin (2θ + α) where r > 0 and 0 < α < π/2.
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- 3(a)(i)Prove that (cot y - cot x)/(cot x + cot y) = sin(x - y)/sin(x + y).[4 marks]
- 3(a)(ii)Hence, or otherwise, find the possible values for y in the trigonometric equation (cot y - cot x)/(cot x + cot y) = 1, 0 ≤ y ≤ 2π, when sin x = 1/2, 0 ≤ x ≤…[8 marks]
- 3(b)(ii)a)Hence, or otherwise, determine the value of θ, between 0 and 2π radians, at which f(θ) is a minimum[4 marks]
- 3(b)(ii)b)the minimum and maximum values of 1/(7-f(θ))[5 marks]
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