3 marksTrigonometric Functions, Identities and Equations

CAPE Pure Mathematics Unit 1 · May/June 2001 · Paper 2 · Question 2(c)(i)

The parametric equations of a curve, C, are 2x = cot θ - cosec θ and 4y = cosec θ - 2 cot θ.

Express cot θ and cosec θ in terms of x and y.

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Other parts of this question

2(a)(i)Express f(x) in the form p(x-q)² + r, where p, q, r ∈ R.[3 marks]
2(a)(ii)Sketch the graph of f(x).[2 marks]
2(a)(iii)Hence, or otherwise, find the turning point of the graph and determine whether it is a maximum or a minimum.[3 marks]
2(b)Given that δ is an acute angle such that cos δ = (1/4)x, find the expression for sin 2δ in terms of x.[4 marks]
2(c)(ii)Find an equation connecting x and y.[2 marks]
2(d)(i)Sketch, in separate diagrams, the graphs of y = sin x and y = cos x for -2π ≤ x ≤ 2π.[6 marks]
2(d)(ii)State clearly the transformation which maps y = cos x onto y = sin x.[2 marks]

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