2023 SCSS P1 Q7

The following trigonometric function models the depth of water motion along Kallang River.

\(y=a\sin(bt)+c\)

\(y\) is the depth of water, \(t\) is time in hours and \(a\), \(b\) and \(c\) are constants.

At high tide, the depth of water is 2.7 m. Six hours later, at low tide, the depth of water is 0.1 m.

This diagram shows part of the above trigonometric function.

1. Find the values of \(a\), \(b\) and \(c\).[4]
2. Find the depth of water after 16 hours.[2]
3. Kayaking is permitted when the depth of water is at least 1.4 m. State the time interval(s) between 0 hour and 12 hours where kayaking is permitted.[1]