The depth of water in a harbour hours after midnight is metres.

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

The depth of water in a harbour

t

hours after midnight is

d(t)=4\cos\left(\frac{\pi}{6}t\right)+6

metres. (1) Sketch the graph of

d

against

t

for

0\leq t\leq24

. (2) Find the highest and lowest depths of the water, and the times at which they occur. (3) A boat requires a water depth of

5

metres to sail in. Will the boat be able to enter the harbour at

8\,\text{pm}