SOLUTION: Very confused, Please explain how this works I have to make a graph for this sine function: g(x) = -2sin(πx+π/3) I know what the graph looks like but I need to know

Algebra ->  Trigonometry-basics -> SOLUTION: Very confused, Please explain how this works I have to make a graph for this sine function: g(x) = -2sin(πx+π/3) I know what the graph looks like but I need to know       Log On


   

Question 920682: Very confused, Please explain how this works
I have to make a graph for this sine function:
g(x) = -2sin(πx+π/3)
I know what the graph looks like but I need to know how to make it myself
I found:
Amp = 2
Period = 2
Phase shift = -1/3
I know the end position is 5/3 because -1/3+2/1 = 5/3. Right?
What determines the points from -1/3 to 5/3 on the x-axis?

And from -1/3 I don't know where the line enters the y-axis I know the range is between 2 and -2 but when I see the graph it shows the line going from -1/3 and entering above the -2, why is this? Please I really need help on this
Thank you
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
What you worked out is useful and correct.
I would look at it like this:
I know what f%5B1%5D%28x%29=sin%28%28x%29%29 looks like.
It looks like this graph%28900%2C300%2C-0.5%2C8.5%2C-1.5%2C1.5%2Csin%28x%29%29 ,
crossing the x-axis at x=0 , x=pi , x=2pi , and so on.
Making it f%5B2%5D%28x%29=sin%28%28pi%2Ax%29%29 compresses it horizontally a bit,
very conveniently making it cross the x-axis at x=0 , x=1 , x=2 , etc:
graph%28900%2C300%2C-1%2C8%2C-1.5%2C1.5%2C2%2Csin%28pi%2Ax%29%29 .
Then, f%5B3%5D%28x%29=f%5B2%5D%28x%2B1%2F3%29=sin%28pi%2A%28x%2B1%2F3%29%29=sin%28pi%2Ax%2Bpi%2F3%29
crosses the x-axis when
x%2B1%2F3=0<--->x=-1%2F3 ,
x%2B1%2F3=1<--->x=1-1%2F3=2%2F3 ,
x%2B1%2F3=2<--->x=2-1%2F3=5%2F3 , etc.
In fact the graph of red%28f%5B3%5D%29%28x%29=f%5B2%5D%28x%2B1%2F3%29=sin%28pi%2A%28x%2B1%2F3%29%29=sin%28pi%2Ax%2Bpi%2F3%29
looks just like the graph of green%28f%5B2%5D%29%28x%29=sin%28%28pi%2Ax%29%29 ,
but with all the points moved 1%2F3 to the left:
graph%28900%2C300%2C-1%2C8%2C-1.5%2C1.5%2Csin%28pi%2Ax%2Bpi%2F3%29%2Csin%28pi%2Ax%29%29 .
Now, the graph of blue%28g%28x%29%29=-2%2Ared%28f%5B3%5D%29%28x%29=-2%2Asin%28pi%2Ax%2Bpi%2F3%29
Is similar, but twice as tall (stretched vertically, and flipped about the x-axis:
.