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1 Pure Mathematics

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Question 301
a.

Given that θ \theta\,θ is small and measured in radians, show that

sin⁡4θ−tan⁡2θθ(1−cos⁡3θ)\displaystyle \frac{\sin 4\theta - \tan 2\theta}{\theta\left(1 - \cos 3\theta\right)}θ(1−cos3θ)sin4θ−tan2θ​

can be approximated by Aθ2\dfrac{A}{\theta^2}θ2A​, where A A\,A is a constant to be found.

[4]
b.

Use your answer to part (a) to estimate the value of the expression when θ=0.02\theta = 0.02θ=0.02.

[1]
c.

Explain why the approximation becomes less reliable as θ \theta\,θ increases.

[1]
Markscheme

1 Pure Mathematics Questions

  1. A Level
  2. /Maths
  3. /1 Pure Mathematics

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