SOLUTION: I need to find the amplitude, period, phase shift and translation as well as graph y=2sin(3x-pi/2)-1

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Question 763669: I need to find the amplitude, period, phase shift and translation as well as graph y=2sin(3x-pi/2)-1
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
y=2sin%283x-pi%2F2%29-1 --> y=2sin%283%28x-pi%2F6%29%29-1

Let's start with the simplest related function.
The graph for y=sin%28x%29 is graph%28400%2C200%2C-1%2C7%2C-2%2C2%2Csin%28x%29%29. Its period is 2pi.
graph%28400%2C200%2C-1%2C7%2C-2%2C2%2Csin%283x%29%29 is the graph of y=sin%283x%29, whose period is highlight%28period=2pi%2F3%29.
Substituting x-pi%2F6 for x translates the function highlight%28pi%2F6%29 units to the highlight%28right%29. That's the phase shift.
So, graph%28400%2C200%2C-1%2C7%2C-2%2C2%2Csin%283%28x-pi%2F6%29%29%29 is the graph of y=sin%283%28x-pi%2F6%29%29 (with the same period).
A factor of 2 in front dilates the graph vertically to get highlight%28amplitude=2%29, and the -1 added at the end translates the function highlight%28down%29 by highlight%281%29 unit:
graph%28400%2C300%2C-1%2C7%2C-4%2C2%2C2sin%283%28x-pi%2F6%29%29-1%2C-1%29