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1 Pure Mathematics

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Question 798
a.

For a small angle θ\thetaθ, where θ \theta\,θ is measured in radians, show that

2cos⁡θ+(sin⁡θ+1)2≈2θ+32\cos\theta + (\sin\theta + 1)^2 \approx 2\theta + 32cosθ+(sinθ+1)2≈2θ+3

[3]
b.

Hence determine an approximate solution of the equation

2cos⁡θ+(sin⁡θ+1)2=20tan⁡θ2\cos\theta + (\sin\theta + 1)^2 = 20\tan\theta2cosθ+(sinθ+1)2=20tanθ

where θ \theta\,θ is small and positive.

[2]
Markscheme

1 Pure Mathematics Questions

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