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 OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.