1.8 E: Trigonometry

Given that $\theta\,$ is small and measured in radians, show that

$sin⁡4θ−tan⁡2θθ(1−cos⁡3θ)\displaystyle \frac{\sin 4\theta - \tan 2\theta}{\theta\left(1 - \cos 3\theta\right)}$

can be approximated by $Aθ2\dfrac{A}{\theta^2}$ , where $A\,$ is a constant to be found.

[4]

Use your answer to part (a) to estimate the value of the expression when $θ=0.02\theta = 0.02$ .

[1]

Explain why the approximation becomes less reliable as $\theta\,$ increases.

[1]

Given that $\theta\,$ is small and measured in radians, show that

$sin⁡4θ−tan⁡2θθ(1−cos⁡3θ)\displaystyle \frac{\sin 4\theta - \tan 2\theta}{\theta\left(1 - \cos 3\theta\right)}$

can be approximated by $Aθ2\dfrac{A}{\theta^2}$ , where $A\,$ is a constant to be found.

Use your answer to part (a) to estimate the value of the expression when $θ=0.02\theta = 0.02$ .

[1]

Explain why the approximation becomes less reliable as $\theta\,$ increases.

[1]

1.8 E: Trigonometry Questions