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.

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
**Hence**
$$D(t)=5-sin({{\pi t}\over 6})$$