CAPE Pure Mathematics Unit 1 · May/June 2013 · Paper 2 · Question 3(b)(i)
Express f(θ) = 3 cos θ – 4 sin θ in the form r cos (θ+ α) where r > 0 and 0° ≤ α ≤ π/2.
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- 3(a)(i)Show that sin 2θ = (2 tan θ) / (1 + tan² θ)[4 marks]
- 3(a)(ii)Hence, or otherwise, solve sin 2θ – tan θ = 0 for 0 ≤ θ ≤ 2π.[8 marks]
- 3(b)(ii)Hence, find[1 mark]
- 3(b)(ii)a)the maximum value of f(θ)[2 marks]
- 3(b)(ii)b)the minimum value of 1 / (8+f(θ))[2 marks]
- 3(b)(iii)show that[1 mark]
- 3(b)(iii)a)sin A = sin (B + C)[3 marks]
- 3(b)(iii)b)sin A + sin B + sin C = sin (A + B) + sin (B + C) + sin (A + C).[2 marks]
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