Describe how to transform the graph of $y=\sin x$ to $y=-\sin \left(\frac{1}{3}x\right)$.

After you exercise, the velocity of air flow(in $\mathrm{litres}$ per $\mathrm{second}$) into your lungs can be modelled by the equation $y=2\sin \left(90°t\right)$.

Draw the graph of the function in the first $8 \mathrm{seconds}$.

When you ride a Ferris wheel, your vertical height above the ground changes. The relationship between your height above the ground and the time for a complete revolution of the wheel can be modelled with the sinusoidal graph given below. Find a function that models the graph.

The height in meters of the tide above the mean sea level on one day at Bal Harbour can be modelled by the function $h\left(t\right)=3\sin 30°t$, where $t$ is the number of hours after midnight. A ship can cross the harbour if the tide is at least $2 \mathrm{m}$ above the average sea level. Determine the time when it can cross the harbour.

For the following graph, find the amplitude, frequency, and period. Then, write down the equation that represents the function.

A Ferris wheel has a radius of $10$ meters. The bottom of the wheel is $2$ meters above the ground. The wheel, rotating at a constant speed, takes $100$ seconds to complete one revolution. Draw a graph of your function.

A tsunami, or monster tidal wave can have a period anywhere between $10$ minutes and $2$ hours, with a wavelength well over $500 \text{km}$. Because of its incredible destructive powers, warning systems have been developed in regions where tsunamis are most likely to happen. A particular tsunami to hit a coastal town in Japan had a period of about quarter of an hour. The normal ocean depth in this town was $9 \text{m}$, and a tsunami of amplitude $10 \text{m}$hit the coast. Write a sinusoidal function to describe the relationship of the depth of water and time, given  that when $t=0,$ the sinusoidal function is at minimum. Use this function to predict the depth of the water after $10$ minutes.