Model and solve problems that involve trigonometric functions, with and without technology.

A Ferris wheel at a local carnival has a diameter of 18 m and its lowest point is 2 m above ground level. The wheel completes one full rotation every 20 seconds. At time t = 0 seconds, a passenger is at the lowest point of the wheel. Determine the equation for the height h(t) of the passenger above ground level in the form h(t) = a cos(bt + c) + d or h(t) = a sin(bt + c) + d.

The depth of water in a harbour, d(t) metres, is modelled by the function d(t) = 8 + 3sin(πt/6), where t is the time in hours after midnight. Determine when the water depth first reaches 11 metres.

A population of migratory birds returns to a wetland reserve each year. The number of birds present at time $t$ months after arrival is modelled by the function $$N(t) = 8{,}500 + 3{,}200\sin\left(\frac{\pi t}{6}\right)$$ where $t$ is measured in months and $0 \le t \le 12$. (a) Calculate the maximum number of birds present at the reserve. [1 mark] (b) Find the values of $t$ (in months) at which the number of birds equals 8{,}500. [2 marks]