Given that θ \theta\,θ is small and measured in radians, show that
sin4θ−tan2θθ(1−cos3θ)\displaystyle \frac{\sin 4\theta - \tan 2\theta}{\theta\left(1 - \cos 3\theta\right)}θ(1−cos3θ)sin4θ−tan2θ
can be approximated by Aθ2\dfrac{A}{\theta^2}θ2A, where A A\,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 = 0.02θ=0.02.
Explain why the approximation becomes less reliable as θ \theta\,θ increases.
225 exam-style questions on WJEC A Level Maths 3.5 Trigonometry (A-level only), covering 3.5.1 Trigonometry (A-level only), 3.5.2 Trigonometry (A-level only), 3.5.3 Trigonometry (A-level only), 3.5.4 Trigonometry (A-level only), 3.5.5 Trigonometry (A-level only), 3.5.6 Trigonometry (A-level only), 3.5.7 Trigonometry (A-level only), and 3.5.8 Trigonometry (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.