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Question 106
a.

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

8cos⁡(θ)+cos⁡2(4θ)≈9−20θ2+64θ4 8 \cos(\theta) + \cos^2(4\theta) \approx 9 - 20\theta^2 + 64\theta^4 8cos(θ)+cos2(4θ)≈9−20θ2+64θ4
[3]
b.

Hence find an approximation of 8cos⁡(θ)+cos⁡2(4θ)8 \cos(\theta) + \cos^2(4\theta)8cos(θ)+cos2(4θ) when θ=3∘\theta = 3^\circθ=3∘, giving your answer to 3 significant figures

[2]
c.

Calculate the percentage error in your approximation

[2]
Markscheme

Radians Questions

  1. A Level
  2. /Maths
  3. /Radians

278 exam-style questions on Edexcel A Level Maths Radians, covering 5.1 Radian Measure, 5.2 Arc Length, 5.3 Areas of Sectors and Segments, 5.4 Solving Trigonometric Equations, and 5.5 Small Angle Approximations. Each one has a worked solution and a mark scheme showing where the marks go.

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