Writing Sin Equation Homework: Finding Amplitude, Upward Shift & Phase Shift

[Miike012]

Homework Statement

I have to fill in the missing info...
Y=A*Sin[B(x-c)] +D

A = 3. For finding the amplitude all I have to do it multiply 1/2 by the range?
D = 3. For finding upward shift all I have to do is see if the center has moved up?
period = 4pi/3 so B = 3/2

I am confused on how to find the phase shift... can I implement a,b, and d into my equation and solve for C somehow?

By just looking at the picture is looks like c could eaither be + or - pi/3 ?
But I would like to solve for this algebraically.

 

[eumyang]

A = 3. For finding the amplitude all I have to do it multiply 1/2 by the range?

I think of it as half the height of the wave.

D = 3. For finding upward shift all I have to do is see if the center has moved up?
period = 4pi/3 so B = 3/2

Ok and ok

I am confused on how to find the phase shift... can I implement a,b, and d into my equation and solve for C somehow?
By just looking at the picture is looks like c could eaither be + or - pi/3 ?
But I would like to solve for this algebraically.

Why? I would just look at the graph. The phase shift is the horizontal translation. A positive value of C would mean a horizontal shift to the right, while a negative value of C would mean a horizontal shift to the left. So which value of C is it? π/3 or -π/3?