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6 marksTrigonometric Functions, Identities and Equations

CAPE Pure Mathematics Unit 1 · May/June 2017 · Paper 2 · Question 3(a)(ii)

Given that sin A = 3/5 and cos B = -1/2, where angle A is acute and angle B is obtuse, express tan (A + B) in the form a + b√3, where a and b are real numbers.

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  1. 3(a)(i)Prove the identity tan(A + B) = (tan(A) + tan(B))/(1 - tan(A)tan(B)).[4 marks]
  2. 3(b)Solve the equation sin²θ - 2cos²θ + 3cosθ + 5 = 0 for 0 ≤ θ ≤ 4π.[6 marks]
  3. 3(c)(i)Express f(θ) = 6cosθ + 8sinθ in the form r sin(θ + α) where 0 ≤ α ≤ 90°.[3 marks]
  4. 3(c)(ii)Hence, or otherwise, find the general solution of f(θ) = 2.[6 marks]

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