The displacement of a vibrating plate, DDD millimetres, is modelled by the function D(t)=7sint−24cost+30,t≥0D(t) = 7 \sin t - 24 \cos t + 30, \quad t \ge 0D(t)=7sint−24cost+30,t≥0 where 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 Edexcel A Level Maths 7.4 Simplifying a cos x +- b sin x with exam-style questions for A Level Maths. 19 questions, matched to the Edexcel A Level Maths (9MA0) 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.