Ive been trying to figure this out but need help!

Question

Suppose the tide rises 9.5 feet above and below mean sea-level (0 feet). The tide pattern repeats every 12 hours (there are two high tides and two low tides per day). Answer the following if the tide is at its lowest point at 2:00am.

a. Draw an accurate graph showing the high and low tides for at least a 12 hour period.

b. Find a formula giving the height of the tide (relative to mean sea-level) as a function for the number hours since midnight (midnight is x = 0).

c. What is the tide level at 7am?

    - Use your function to show how you arrived at your result. If applicable, round your result to the nearest tenth of a foot.

    - Plot and label this point on your graph in part a.

Answer 1

This is a sine curve.

a sin ( b (x-c)) + d.

mean sea level = 0 feet , so d=0

rises 9.5 above so a = 9.5

repeats every 12 hours, so period = 12. b = 2π/ period, so b = π/6

lowest point at 2 am.

A standard sine curve (with c=0) has it's lowest point 3/4 way through the period ie at t=9 here (as the period is 12).

We need the lowest point to be 7 hours earlier (at 2 am)

So set c = -7 (this moves the sine curve 7 units to the left)

So your equation will be

9.5 sin ( (π/6) (t+7)) where t is the hours after midnight

(you can draw this on Desmos and make sure it fits. Make sure Desmos is set to radians).

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For (c) put t=7 into your function