Trigonometric Functions · Paper 1 — Free Maths AA SL Practice Questions

A water sprinkler rotates back and forth. The horizontal distance $d$ (in metres) from the sprinkler to the water jet's landing point is modelled by $$d(\theta) = 15\sin(2\theta)$$ where $\theta$ is the angle of the sprinkler head from the vertical, in radians.

A ladder of length $5$ metres leans against a vertical wall. The angle between the ladder and the ground is $\theta$, where $0 < \theta < \dfrac{\pi}{2}$. The horizontal distance from the base of the ladder to the wall is $x$ metres and the vertical height reached by the ladder is $h$ metres.

The graph of $y = a\cos(bx) + c$ for $0 \leq x \leq 2\pi$ has a maximum point at $(0,\, 5)$ and a minimum point at $(\pi,\, -1)$.

A water wheel of radius $5$ metres rotates anticlockwise at a constant angular speed. The point $P$ is located at the lowest point on the wheel at time $t = 0$ seconds. The height $h(t)$ metres of $P$ above the water level is modelled by $$h(t) = a\sin(bt) + c, \quad t \geq 0$$ After $2$ seconds, $P$ reaches its maximum height of $8$ metres for the first time.