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1.8 E: Trigonometry

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Question 40
a.

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

2cos⁡(3θ)+cos⁡2(θ)≈3−10θ2+0.25θ4 2 \cos(3\theta) + \cos^2(\theta) \approx 3 - 10\theta^2 + 0.25\theta^4 2cos(3θ)+cos2(θ)≈3−10θ2+0.25θ4
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b.

Hence find an approximation of 2cos⁡(3θ)+cos⁡2(θ)2 \cos(3\theta) + \cos^2(\theta)2cos(3θ)+cos2(θ) when θ=6∘\theta = 6^\circθ=6∘

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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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