# Finding a trigonometric function for a problem

The question: At Dolphin Bay the depth of the water at the end of the jetty is 6 metres at high and 4 metres at low tide. High tide occurs at 11am and low tide occurs at 5pm.

a). Using the information given find a trigonometric function which models the depth of the water at the end of the jetty.

b. Find the depth of the water at 12:30pm.

c). A boat moored at the end of the jetty needs to leave the Bay before the depth of the water falls to 4 metres. At what time after the 11am high tide will the depth of the water be 4 metres?

d). Find the next time after low tide when the depth of the water will again be 4 metres.

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Define your time variable specifically: What are the units? What time does $t = 0$ refer to? (These are arbitrary choices, but write down your choices). – Sammy Black Oct 20 '13 at 9:12
What is the equilibrium height of the water? The sinusoidal function will fluctuate above and below this height. Once you know this height, you should be able to determine the amplitude of the fluctuations. – Sammy Black Oct 20 '13 at 9:14
What is the period (one complete cycle) of the tides? How do you modify a standard sinusoidal function (with period $2\pi$) to have the correct period? – Sammy Black Oct 20 '13 at 9:16

A way of representing the trigonometric function which models the depth of the water is: $$5-Asin(2\pi {t\over T})$$ Where:
$t=0$ is considered to be 2 pm
$A=1$ -The Amplitude
$T=12$-The time period
$$D(t)=5-sin({{\pi t}\over 6})$$