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) (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 .
The factor B multiplying the variable in that parenthesis is related to the period (P) by
The angle measure is the phase shift, showing how far ahead (angle-wise) is the shifted function with respect to the "unshifted" .
(Physicist, electricians and electrical engineers are concerned with those angles).
So would be the equation for a sine curve with amplitude 3, period and phase shift .
The horizontal shift of the curve would be more complicated.
The graph would be horizontally shifted to the right by . and 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 for with a period of 2, a horizontal shift of and a phase shift of .
We can also shift the curve up or down, as in the graph below, shifted up by 1 unit for .
