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

3cos⁡(2θ)+cos⁡2(θ)≈4−7θ2+0.25θ4 3 \cos(2\theta) + \cos^2(\theta) \approx 4 - 7\theta^2 + 0.25\theta^4 3cos(2θ)+cos2(θ)≈4−7θ2+0.25θ4
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b.

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

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c.

Calculate the percentage error in your approximation

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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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