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1.8 E: Trigonometry

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Question 43

You may use the identity cos⁡3θ≡4cos⁡3θ−3cos⁡θ\cos 3\theta \equiv 4\cos^3\theta - 3\cos\thetacos3θ≡4cos3θ−3cosθ.

a.

Show that the equation 1−cos⁡3x=sin⁡2x1 - \cos 3x = \sin^2 x1−cos3x=sin2x can be written as

cos⁡x(4cos⁡x+3)(cos⁡x−1)=0\cos x\left(4\cos x + 3\right)\left(\cos x - 1\right) = 0cosx(4cosx+3)(cosx−1)=0

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b.

Hence solve, for −π≤x≤π-\pi \leq x \leq \pi−π≤x≤π, the equation

1−cos⁡3x=sin⁡2x1 - \cos 3x = \sin^2 x1−cos3x=sin2x

Give your answers to three significant figures where they are not exact.

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Markscheme

1.8 E: Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.8 E: Trigonometry

317 exam-style questions on AQA A Level Maths 1.8 E: Trigonometry, covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context. Each one has a worked solution and a mark scheme showing where the marks go.

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