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2 marksThe Real Number System – ℝ

CAPE Pure Mathematics Unit 1 · May/June 2011 · Paper 2 · Question 4(c)(iii)

Using the results in (c)(i) and (ii) above.

Evaluate Σ (from r=1 to n) (tan rθ sin 2rθ + cos 2rθ) where n is a positive integer.

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Other parts of this question

  1. 4(a)By using x = cos²θ, or otherwise, find all values of the angle θ such that 8 cos³θ - 10 cos²θ + 3 = 0, for 0 ≤ θ ≤ π.[6 marks]
  2. 4(b)(i)Find, in terms of θ, the length of the side BC.[2 marks]
  3. 4(b)(ii)Find the value of θ if |BC| = 7 cm.[5 marks]
  4. 4(b)(iii)Is 15 a possible value for |BC|? Give a reason for your answer.[2 marks]
  5. 4(c)(i)Show that (1 - cos 2θ) / sin 2θ = tan θ.[3 marks]
  6. 4(c)(ii)a)Show that (1 - cos 4θ) / sin 4θ = tan 2θ.[3 marks]
  7. 4(c)(ii)b)Show that (1 - cos 6θ) / sin 6θ = tan 3θ.[2 marks]

More practice: the rest of this paper · more The Real Number System – ℝ questions · all CAPE Pure Mathematics Unit 1 past papers