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6 marksTrigonometric Functions, Identities and Equations

CAPE Pure Mathematics Unit 1 · May/June 2009 · Paper 2 · Question 4(a)(ii)

A quadrilateral ABCD has AB = 4 cm, BC = 9 cm, AD = x cm, ∠BAD = ∠BCD = θ, and ∠CDA is a right-angle, as shown in a diagram not drawn to scale.

By expressing x in the form r cos (θ – α), where r is positive and 0 < α < π/2, find the MAXIMUM possible value of x.

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Other parts of this question

  1. 4(a)(i)Show that x = 4 cos θ + 9 sin θ.[4 marks]
  2. 4(b)(i)Find, without using tables or calculators, the EXACT values of sin (A + B).[3 marks]
  3. 4(b)(ii)Find, without using tables or calculators, the EXACT values of cos (A - B).[3 marks]
  4. 4(b)(iii)Find, without using tables or calculators, the EXACT values of cos 2A.[2 marks]
  5. 4(c)Prove that tan (x/2 + π/4) = sec x + tan x.[7 marks]

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