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1 Pure Mathematics

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Question 730
a.

When θ \theta\,θ is small and measured in radians, show that cos⁡θsin⁡θ\dfrac{\cos\theta}{\sin\theta}sinθcosθ​ can be approximated by 2−θ22θ\dfrac{2 - \theta^2}{2\theta}2θ2−θ2​.

[3]
b.

Hence find an approximate value for cos⁡π24sin⁡π24\displaystyle \dfrac{\cos\frac{\pi}{24}}{\sin\frac{\pi}{24}}sin24π​cos24π​​.

[2]
c.

Calculate the percentage error in your approximation, giving your answer to two significant figures.

[1]
Markscheme

1 Pure Mathematics Questions

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