At what time will the tide be 14 feet

Question

At what time will the tide be 14 feet? The tide near lake erie, ehere sully is from, can be modeled by d=35-28cos(pi/6.2)t, where d is the water depth in feet.

Answer 1

14 = 35 - 28cos(pi/6.2)t

 

28cos(pi/6.2)t = 35 - 14 = 21

 

cos(pi/6.2)t = 21/28 = 3/4

 

Arccos (3/4) = 0.7227

 

0.7227 = pi/6.2 t

 

1.4271 = t

 

You haven't given units for time in the equation, but presumably they are in hours.

 

This answer lies in the I Quadrant, because that is the range of the Arccosine function.  There is an equally valid answer in the IV Quadrant of -1.4271.

 

If the units are hours, and a tide cycle is 24 hours, then the other time would be  22.5729

 

Converting to time in hours, minutes, and seconds the times are

1:25:38  and 22:34:22