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

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The discussion centers on solving a sine equation of the form Y=A*Sin[B(x-c)] +D, with specific values for amplitude (A=3), upward shift (D=3), and period (B=3/2). The user is seeking clarification on calculating the phase shift (C) and is uncertain whether it should be +π/3 or -π/3. It is noted that the phase shift represents a horizontal translation, where a positive C indicates a right shift and a negative C indicates a left shift. The user expresses a desire to solve for C algebraically rather than relying solely on visual interpretation from a graph. The conversation emphasizes the importance of understanding the relationship between the parameters and their impact on the sine function's graph.
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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.
 

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Miike012 said:
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?
 

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