5.5 Small Angle Approximations
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a.

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

4cos⁡(θ)+cos⁡2(2θ)≈5−6θ2+4θ4 4 \cos(\theta) + \cos^2(2\theta) \approx 5 - 6\theta^2 + 4\theta^4 4cos(θ)+cos2(2θ)≈5−6θ2+4θ4
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b.

Hence find an approximation of 4cos⁡(θ)+cos⁡2(2θ)4 \cos(\theta) + \cos^2(2\theta)4cos(θ)+cos2(2θ) when θ=3∘\theta = 3^\circθ=3∘

[2]
c.

Calculate the percentage error in your approximation

[2]

5.5 Small Angle Approximations Questions

Practise Edexcel A Level Maths 5.5 Small Angle Approximations with exam-style questions for A Level Maths. 25 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

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5.5 Small Angle Approximations Questions

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