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Question 19
a.

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

6cos⁡(θ)+cos⁡2(2θ)≈7−7θ2+4θ4 6 \cos(\theta) + \cos^2(2\theta) \approx 7 - 7\theta^2 + 4\theta^4 6cos(θ)+cos2(2θ)≈7−7θ2+4θ4
[3]
b.

Hence find an approximation of 6cos⁡(θ)+cos⁡2(2θ)6 \cos(\theta) + \cos^2(2\theta)6cos(θ)+cos2(2θ) when θ=4∘\theta = 4^\circθ=4∘

[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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