The function f(t) = 4 cos(pi over 3t) + 15 represents the tide in Bright Sea. It has a maximum of 19 feet when time (t) is 0 and a minimum of 11 feet. The sea repeats this cycle every 6 hours. After five hours, how high is the tide?

Question

anonymous · Answer

@AkashdeepDeb

akashdeepdeb · Answer

You should understand some cool things here.

A wave looks like a sine wave/cosine wave and that is why its height is given as a function of the cosine of time. 

Plus, we know that the cosine function f(x) = cos x can have the maximum value and the minimum value +1 and -1 respectively. So that is the reason the maximum height is 19 feet and 11 feet. 

Because max of f(t) = 4(+1) + 15 = 19 ft
Because min of f(t) = 4(-1) + 15 = 11 ft

NOW TRY THE QUESTION. Do you see any patterns? Try drawing the graph. :D

anonymous · Answer

I see a pattern in trying to figuring out the maximum and minimum. How you showed you solved it.

anonymous · Answer

Other than that I do really know how to solve it :/ a lot of what you said makes sense I just don't know how to put it together.