First High & Low Tide in Harbor: Water Depth at 12am & 6pm

[TonyC]

Suppose the depth of the tide in a certain harbor can be modeled by y=21-5cos pi t/6, whre y is the water depth in feet and t is the time in hours. Consider a day in which t=0 represents 12:00 midnight. For that day, when are the first high tide and the first low tide and what is the water depth at each time?

 

[VietDao29]

You have:
$$-1 \leq \cos \alpha \leq 1$$
So what can you say about the $$y = 21 - 5 \cos \frac{\pi t}{6}$$
Viet Dao,

 

[TonyC]

What are you looking for?

 

[VietDao29]

Okay, when y is minimum, that means:
$$5 \cos \frac{\pi t}{6}$$ is maximum.
So $$\cos \frac{\pi t}{6}$$ is maximum.
So y is minimum means that $$\cos \frac{\pi t}{6}$$ is maximum.
$$-1 \leq \cos \frac{\pi t}{6} \leq 1$$ so what t makes $$\cos \frac{\pi t}{6}$$ maximum?
Viet Dao,

 

[mathmike]

you can take the first derivative and then find when it is 0 to tell you where your critical points are then use that to find the min and max