MATH QUESTION PLSSS HELP

Question

Due to the tide, the depth of water at a dock rises and falls over the course of the day. The depth can be modeled by the following equation:

f(t)=4sin⁡(π/12t)+7

If you want to tie up your boat at the dock, the water needs to be nine feet deep. If the time is currently t=0, at what time will you be able to tie up your boat? Choose the closest time.

t= ?

Answer 1

f(t) = 4sin(πt/12)+7

When the water is 9 feet deep

4sin(πt/12)+7 = 9

4sin(πt/12) = 2

sin(πt/12) = 1/2

When sin(x) = 1/2, x = π/6

πt/12 = π/6

t = (π/6)(12/π) = 12/6 = 2 hours