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1.5.5 Small angle approximations (A-level only)

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Question 1
60%
a.

When θ \theta\,θ is small, show that cos⁡θsin⁡θ\displaystyle \frac{\cos \theta}{\sin \theta}sinθcosθ​ can be approximated by 2−θ22θ\displaystyle \frac{2 - \theta^2}{2\theta}2θ2−θ2​

[3]
b.

Hence, approximate the value of cos⁡π24sin⁡π24\displaystyle \frac{\cos \frac{\pi}{24}}{\sin \frac{\pi}{24}}sin24π​cos24π​​

[2]
c.

Calculate the percentage error in your approximation

[2]

1.5.5 Small angle approximations (A-level only) Questions

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  3. /1.5.5 Small angle approximations (A-level only)