Question

On a typical day at an ocean port, the water has a maximum depth of 20m at 8:00AM. The minimum depth of 8m occurs 6.2h later. Assume that the relation between the depth of the water and time is a sinusoidal function.

write an equation for the depth of the water at any time, t hours

I got h=6cos(2pi((t-8)/12.4))+14

how do I get the equation for sin?
I got h=6sin(2pi((t-9.8)/12.4))+14
since the highest point is at 8:00AM, and calculated the lowest point would be at 1:48AM(1.8@x-axis). Then I did 1.8+8 = 9.8 for the phase shift

but the back of the book says
h=6sin(2pi((t-4.9)/12.4))+14

thanks in advance

Answer 1

If high tide is at 8 am

and the time from high to low is 6.2 hr

then half tide (mid-tide) where the sin function is zero is at 8 - 3.1 = 4.9 am

Answer 2

Oh right, it starts in the middle, thanks!