Write a sine/cosine equation.

Question

Low tide in the ocean occurs at 8:00a.m. The depth of the water at this time is 4 meters. High tide occurs at 4:00 p.m. and the depth of the water at this time is 38 meters. Assume that the 12:00 a.m. (prior to the first low tide) is t=0. Make a table of values for two full cycles. Write a sine/cosine equation for your graph.

 

     t  l  h  

        l

        l

        l

        l

 

 

Answer 1

min = 4

max =38

average = (4+38)/2 = 42/2 =21 = midline = D

A = amplitude = (38-4)/2 =34/2 =17 =38-21=21-4

B = 2pi/period = 2pi/12 =pi/6

h(t) = AsinB(t+C)+D

h(t) = 17sin[(pi/6)(t+C)] + 21

12 am is t=0, 8am is low tide with h=4 when t=8

C= phase shift needed to make h=4 when t=8

h(4) = 17sin[(pi/6)(8+C) +21

sin[(pi/6)(8+C) =-1

(pi/6)(8+C)=270= 3pi/2

4pi/3 +C/4 = 3pi/2

4pi/3-3pi/2 =-C/4

4C= -(8pi-6pi)/6 = -2pi/6 = -pi/3 = -60 degrees

h(t) =17Sin[(pi/6)(8-pi/3)] + 21