CAPE Pure Mathematics Unit 1 · May/June 2024 · Paper 2 · Question 3(a)(i)
Express 5 sin theta + 12 cos theta in the form r sin(theta + alpha), where r > 0 and 0 < alpha < 2*pi.
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- 3(a)(ii)Hence, or otherwise, show that 5 sin theta + 12 cos theta + 7 <= 20.[3 marks]
- 3(b)(i)Show that 2 sin x + 3 cos x = 3 may be written as 13 cos^2 x - 18 cos x + 5 = 0.[5 marks]
- 3(b)(ii)Hence or otherwise, solve the equation 2 sin x + 3 cos x = 3 for -pi <= x <= pi.[5 marks]
- 3(c)Show that (2 cos^2 x - 1)^2 / (cos^4 x - sin^4 x) == 1 - 2 sin^2 x.[6 marks]
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