Trigonometry - Trigonometric Graphs and Parameters

The height of tide, \(y\) m, at a coast on a particular day can be approximated by
\(y = 2 + \cos \left( \frac{\pi}{6} t \right),\) where \(t\) is the time in hours after midnight.

1. Sketch the graph of \(y = 2 + \cos \left( \frac{\pi}{6} t \right)\) for \(0 \le t \le 24\).
2. Find the height of tide at \(7:30\) a.m. on that day.
3. Find the time(s) when the height of tide is \(2.6\) m on that day.
4. Find the interval(s) of time that the height of tide is below \(1.4\) m.