Trigonometric Functions · Paper 1 — Free Maths AI HL Practice Questions

A Ferris wheel has a diameter of $50$ metres. Its lowest point is $2$ metres above the ground. The height $h$ metres of a passenger above the ground after $t$ minutes is modelled by $$h(t) = a\sin(bt) + d, \quad t \geq 0$$ where $a$, $b$, and $d$ are positive constants.

The depth of water, $D$ metres, in a harbour is modelled by the function $$D(t) = 4.5 + 2.8\cos\left(\frac{\pi}{6}t\right)$$ where $t$ is the time in hours after midnight.

A tidal energy company models the height of water, $h$ metres, at a proposed turbine site over time $t$ hours, using the function $$h(t) = 4\sin\!\left(\frac{\pi}{6}t\right) + 6\cos\!\left(\frac{\pi}{6}t\right) + 8, \quad t \geq 0.$$