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Question 72

Given that θ \theta\,θ is small,

a.

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

2cos⁡(θ)+cos⁡2(4θ)≈3−17θ2+64θ4 2 \cos (\theta) + \cos^2 (4\theta) \approx 3 - 17\theta^2 + 64\theta^4 2cos(θ)+cos2(4θ)≈3−17θ2+64θ4
[3]
b.

Hence find an approximation of 2cos⁡(θ)+cos⁡2(4θ)2 \cos (\theta) + \cos^2 (4\theta)2cos(θ)+cos2(4θ) when θ=1∘\theta = 1^\circθ=1∘

[2]
c.

Calculate the percentage error in your approximation

[1]
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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