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1.8 E: Trigonometry

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Question 22
a.

Given that θ \theta\,θ is small, use the small angle approximation of cos⁡θ \cos \theta\,cosθ to show that

5cos⁡(θ)−cos⁡2(2θ)≈4+1.5θ2−4θ4 5 \cos(\theta) - \cos^2(2\theta) \approx 4 + 1.5\theta^2 - 4\theta^4 5cos(θ)−cos2(2θ)≈4+1.5θ2−4θ4
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b.

Hence find an approximation of 5cos⁡(θ)−cos⁡2(2θ)5 \cos(\theta) - \cos^2(2\theta)5cos(θ)−cos2(2θ) when θ=2∘\theta = 2^\circθ=2∘

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c.

Calculate the percentage error in your approximation

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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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