figure shows the depth of water at the end of a boat dock Th

figure shows the depth of water at the end of a boat dock. The depth is 9 feet low tide and 17 feet at high tide. On a certain day, low tide occurs at 6 AM and tide at noon. If y represents the depth of the water times hours after midnight, use cosine function of the form y = A cos Bx + D to model the water\'s depth. Write the equation for this problem in the form y = A cos Bx + D. y = (Type an expression using x as the variable. Type an exact answer, using needed. Use integers of fractions for any numbers in the expression.)

Solution

y = A cos Bx + D

at high tide D + A = 17

D-A = 9

on solving we get

A = 4

D = 13

time period = 12

B = 2pi/ 12 = pi/6

so function is

Y = 4 cos ( pi/6 x ) + 13