Determine an equation using y sin x that models the depth o

Determine an equation using y = sin x that models the depth of water at the Bay of Fundy. (must determine amplitude, period, phase shift) Given the general equation: y = a sin[k(x + d)] + c

Solution

min(y)= 4 and max(y)= 36

amplitude:= a = (36-4)/2= 16

the wave\'s center (36+4)/2= 20

y= 16*sin(k(x+d))+20

the y functio in x=0 is negative and min local hence the first value with (3*Pi)/2

where sin(kx+kd)=-1 x=0 kd=3Pi/2 (*)

where x=24 kx+kd=2Pi a complet cicle

k24+3Pi/2=2Pi>>>>24k=Pi/4

k= (1/24)(Pi/4)

from (*)   

d=144

y=16sin( ((Pi/4)*(1/24)) ( x+144))) )+ 20