Sinusoidal functions (wave problem)

Question

The depth of water in a certain area can be estimated by using this equation:

 

h(t)=-4.3cos(pi/6.35(t+1.6))+8.4

 

A boat requires a depth of 7.2 m to ensure safe passage into the area. The boat must also pass under a bridge. Due to the hight of the boat and that of the bridge. the boat can't pass under the bridge safely if the water is deeper than 12.5 m. What time periods can the boat safely travel under the bridge over the next 24-hour period?

Answer 1

Set h(t) = 7.2 + 12.5 = 19.7

 

Then solve for t in the equation

 

-4.3cos(π/6.35(t + 1.6) + 8.4 = 19.7