The displacement of a vibrating plate, DDD millimetres, is modelled by the function
D(t)=7sint−24cost+30,t≥0 D(t) = 7 \sin t - 24 \cos t + 30, \quad t \ge 0 D(t)=7sint−24cost+30,t≥0where ttt is the time in seconds.
Determine a sequence of transformations which maps the graph of y=sinty = \sin ty=sint onto the graph of y=D(t)y = D(t)y=D(t). Fully justify your answer.
Show that the least value of 1D(t)\frac{1}{D(t)}D(t)1 is 155\frac{1}{55}551.
Find the greatest value of 1D(t)\frac{1}{D(t)}D(t)1.
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.