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.
Practise AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions 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, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
