Question

Every day the ocean has two low tides and two high tides. Function g represents the height, in feet, of the water level in a cove relative to theaverage sea level. Let t represent the number of hours elapsed since the water height was equal to the average sea level after a low tide.s(e) = ssin(}t)Plot the points where s(4) is equal to the average sea level.

Answer 1

We can see from the question that we have the sine function, which is modeling the water level in a cove relative to the average sea level, and this function is given by:

$g(t)=4sin(\frac{\pi}{6}t)$

And we need to find the points where g(t) is equal to the average sea level.

1. To find it, we need to analyze the given function as follows:

2. Then we can say that the function has:

• An amplitude (the value from the ,midline of the function, in this case, x = 0,).

,

• The period of the function is given by:

$\begin{gathered} \text{ Period=}\frac{2\pi}{B} \\ \\ \text{ Period=}\frac{2\pi}{\frac{\pi}{6}}=2\pi(\frac{6}{\pi})=12 \\ \\ \text{ Period=}12 \end{gathered}$

3. These values can be seen as follows:

4. To find the points where g(t) is equal to the average sea level, we can see that the average sea level is represented by the midline, x = 0, and from the graph, we can see that these points are points on the x-axis, and they are (6, 0), and (12, 0) for the given graph: