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3.5.2 Trigonometry (A-level only)

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Question 12
a.

When θ \theta\,θ is small, show that cos⁡θ2sin⁡θ\displaystyle \frac{\cos \theta}{2\sin \theta}2sinθcosθ​ can be approximated by 2−θ24θ\displaystyle \frac{2 - \theta^2}{4\theta}4θ2−θ2​

[3]
b.

Hence, approximate the value of cos⁡π302sin⁡π30\displaystyle \frac{\cos \frac{\pi}{30}}{2\sin \frac{\pi}{30}}2sin30π​cos30π​​

[2]
c.

Calculate the percentage error in your approximation

[2]

3.5.2 Trigonometry (A-level only) Questions

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