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4 marksTrigonometric Functions, Identities and Equations

CAPE Pure Mathematics Unit 1 · May/June 1999 · Paper 2 · Question 4(b)(ii)

A diagram shows a triangle ABC where AC = 4 units, CD = 3 units, angle CAB = angle DCB = θ, and AB is perpendicular to CB.

Express AD in the form Rcos(θ + α), where R is positive and α is an acute angle.

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Other parts of this question

  1. 4(a)Given that θ is an obtuse angle such that sin θ = 2/3, find the value of cos 2θ.[2 marks]
  2. 4(b)(i)Obtain an expression for AD in terms of θ.[3 marks]
  3. 4(c)(i)Express cos 3θ in terms of cos θ.[5 marks]
  4. 4(c)(ii)Hence, solve, for 0 < θ < 2π, the equation cos 3θ + 2 cos 2θ + 4 cos θ + 2 = 0.[6 marks]

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