1.8 E: Trigonometry

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

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

[3]

Hence determine an approximate solution of the equation

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

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

[2]

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

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

[3]

Hence determine an approximate solution of the equation

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

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

1.8 E: Trigonometry Questions