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I'm kind of clueless, apart from its a min/max thing. The question is as follows:

The water levels in a dock follow (approximately) a 12-hour cycle, and are modeled by the equation $D = A+ B\sin30t$, where $D$ metres is the depth of water in the dock, $A$ and $B$ are positive constants, and $t$ is the time in hours after 8 a.m.

Given that the greatest and least depths of water in the dock are 7.80m and 2.20m respectively, find the value of A and the value of B

Find the depth of water in the dock at noon, giving your answer correct to the nearest cm.

Thanks in advance.

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What are the min and max values of the sin function. Using this information, can you express the min and max values that D can take on as functions of A and B? Can you then express A and B in terms of the min and max values that D takes on? –  marty cohen Apr 27 '12 at 22:15
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3 Answers

The sine function oscillates between $+1$ and $-1$. So we have $$ A+B\sin (30t) = \begin{cases} 7.8 & \text{when }\sin(30t) = +1 \\ 2.2 & \text{when }\sin(30t) = -1 \end{cases} $$ Therefore $$ \begin{align} A+B & = 7.8 \\ A-B & = 2.2 \end{align} $$ Adding the lefts sides and adding the right sides, we get $2A = 10$, so $A=5$. Then we have $5+B = 7.8$ and $5-B=2.2$, so we conclude that $B=2.8$.

At noon, one-third of the 12 hours have ellapsed, so we plug in the sine of one-third of the circle, i.e. $\sin 120^\circ = \sqrt{3}/2$.

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Hint: what are the maximum and minimum values of $\sin$? What are the depths at the times it hits those values?

It looks like the argument of the $\sin$ function is in degrees, as the period should be about $12$ hours.

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Done! But this can't be done without a calculator; since the last part is found thru 5+1,40*sqrt3 –  Deniz Apr 27 '12 at 22:30
    
You should be able to find A and B without a calculator and it appears you have. Maybe you know that $\sqrt 3 \approx 1.723$, though I agree you should be allowed a calculator if you need this. –  Ross Millikan Apr 27 '12 at 22:44
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Two airplanes leave an airport and the angle between their flight paths is 40 degrees. The first plane had a speed of 300 mph and the other plane has a speed of 200 mph. How far apart are the two planes after 1 hour?

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Is this supposed to be answer to the question? It looks like a new question. Was this posted by accident? –  Amzoti Mar 6 '13 at 23:08
    
This is not an answer to the question. If you have another question, please use the Ask Question link near the upper right of the page. If you have a comment on a question or answer, when you have enough reputation, you can leave a comment. You can always comment on your own question or answer. –  robjohn Mar 7 '13 at 0:10
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