The height, h h\,h metres, of a point on a rotating wind turbine blade above its central axis is modelled by the function
h(t)=5sin(3t) h(t) = 5 \sin(3t) h(t)=5sin(3t)where t t\,t is the time in seconds.
Sketch the graph of h(t)h(t)h(t) for 0≤t≤π0 \le t \le \pi0≤t≤π.
The equation h(t)=kh(t) = kh(t)=k has exactly one solution in the interval 0≤t≤2π3\displaystyle 0 \le t \le \frac{2\pi}{3}0≤t≤32π.
State the possible values of kkk.
317 exam-style questions on AQA A Level Maths 1.8 E: Trigonometry, covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context. Each one has a worked solution and a mark scheme showing where the marks go.