16.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f953fd1c-447f-4e97-a42a-5264c053fda0-32_538_672_219_733}
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\caption{Figure 5}
\end{figure}
A horizontal path connects an island to the mainland.
On a particular morning, the height of the sea relative to the path, \(H \mathrm {~m}\), is modelled by the equation
$$H = 0.8 + k \cos ( 30 t - 70 ) ^ { \circ }$$
where \(k\) is a constant and \(t\) is number of hours after midnight.
Figure 5 shows a sketch of the graph of \(H\) against \(t\).
Use the equation of the model to answer parts (a), (b) and (c).
- Find the time of day at which the height of the sea is at its maximum.
Given that the maximum height of the sea relative to the path is 2 m ,
- find a complete equation for the model,
- state the minimum height of the sea relative to the path.
It is safe to use the path when the sea is 10 centimetres or more below the path.
- Find the times between which it is safe to use the path.
(Solutions relying entirely on calculator technology are not acceptable.)