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4 marksTrigonometric Functions, Identities and Equations

CAPE Pure Mathematics Unit 1 · May/June 2007 · Paper 2 · Question 4(b)(iv)

In the triangle shown below (not drawn to scale), sin q = 3/5 and cos p = 5/13. (Refer to Figure 2).

Determine the exact value of cos (p + t).

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Other parts of this question

  1. 4(a)(i)Prove that cos 2θ = (1 - tan^2 θ) / (1 + tan^2 θ).[4 marks]
  2. 4(a)(ii)Hence, show, without using calculators, that tan 67.5° = 1 + √2.[7 marks]
  3. 4(b)(i)Determine the exact value of cos q.[1 mark]
  4. 4(b)(ii)Determine the exact value of sin p.[1 mark]
  5. 4(b)(iii)Determine the exact value of sin r.[3 marks]

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