Trigonometry question about tides

Question

Suppose the tide rises 8 feet above and below mean sea-level (0 feet). The tide patterns repeat every 12 hours. If the tide is at its lowest point at 6:00am, then find a formula giving the height of the tide (relative to mean sea-level) as a function for the number hours since 6:00am.

Answer 1

First draw a picture with starting point at 6Am. Since you start at the low point this is a negative cosine graph

y= -Acos(bx-c) +d

a= 8

there is no vertical shift or phase shift so c and d are zero

Period = 2pi/b

12 = 2pi/b

b= pi/6 so equation is

y =-8 cos(pi/6)