15. The height of water, \(H\) metres, in a harbour on a particular day is given by the equation
$$H = 4 + 1.5 \sin \left( \frac { \pi t } { 6 } \right) , \quad 0 \leqslant t < 24$$
where \(t\) is the number of hours after midnight, and \(\frac { \pi t } { 6 }\) is measured in radians.
- Show that the height of the water at 1 a.m. is 4.75 metres.
- Find the height of the water at 2 p.m.
- Find, to the nearest minute, the first two times when the height of the water is 3 metres.
(Solutions based entirely on graphical or numerical methods are not acceptable.)