SOLUTION: Write the equation of a sine curve that has an amplitude of 3, a period of and a phase shift of .

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Question 621372: Write the equation of a sine curve that has an amplitude of 3, a period of and a phase shift of .
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Your values for period and phase shift did not get properly rendered. (I cannot see them). However, I can still try yo answer.

The amplitude is the number in front of "sin".
So your equation would be y=3sin%28Bx-phi%29.
The factor B multiplying the variable in that parenthesis is related to the period (P) by B=2pi%2FP
The angle measure phi is the phase shift, showing how far ahead (angle-wise) is the shifted function with respect to the "unshifted" y=3sin%28Bx%29.
(Physicist, electricians and electrical engineers are concerned with those angles).
So y=3sin%28%282pi%2FP%29x-phi%29 would be the equation for a sine curve with amplitude 3, period P and phase shift phi.
The horizontal shift of the curve would be more complicated.
The graph would be horizontally shifted to the right by P%2Aphi%2F2pi .
y=3sin%28%282pi%2FP%29x-phi%29=3sin%28%282pi%2FP%29%2A%28x-phi%2F2pi%29%29 and C=P%2Aphi%2F2pi is what we call the horizontal shift, which is what concerns students graphing curves.
The equations above are for curves "evenly straddling" the x axis, as in
graph%28300%2C200%2C-1.1%2C8.8%2C-3.3%2C3.3%2C3sin%28pi%2A%28x-1%2F6%29%29%29 for y=3sin%28pi%2A%28x-1%2F6%29%29=3sin%28pi%2Ax-pi%2F6%29%29 with a period of 2, a horizontal shift of 1%2F6 and a phase shift of pi%2F6.
We can also shift the curve up or down, as in the graph below, shifted up by 1 unit
graph%28300%2C200%2C-1.1%2C8.8%2C-2.3%2C4.3%2C3sin%28pi%2A%28x-1%2F6%29%29%2B1%29 for y=3sin%28pi%2A%28x-1%2F6%29%29=3sin%28pi%2Ax-pi%2F6%29%2B1%29 .