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3.4 Trigonometry (A-level only)

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Question 71

The displacement of a vibrating plate, DDD millimetres, is modelled by the function

D(t)=7sin⁡t−24cos⁡t+30,t≥0 D(t) = 7 \sin t - 24 \cos t + 30, \quad t \ge 0 D(t)=7sint−24cost+30,t≥0

where ttt is the time in seconds.

a.

Determine a sequence of transformations which maps the graph of y=sin⁡ty = \sin ty=sint onto the graph of y=D(t)y = D(t)y=D(t). Fully justify your answer.

[4]
bi.

Show that the least value of 1D(t)\frac{1}{D(t)}D(t)1​ is 155\frac{1}{55}551​.

[2]
bii.

Find the greatest value of 1D(t)\frac{1}{D(t)}D(t)1​.

[1]

3.4 Trigonometry (A-level only) Questions

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