Question 1146298
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There are several good online graphing tools available to you; and having a good graphing calculator like a TI-83 or TI-84 would be very helpful.<br>
Here is a graph using the tool on this site....<br>
{{{graph(800,400,-5,5,-5,5,3sin(2x-pi))}}}<br>
The general form of a sine function is<br>
{{{a*sin(b(x-c))+d}}}<br>
a is the amplitude
b determines the period: period = 2pi/b
c is the phase (horizontal) shift
d is the vertical shift<br>
Note you have to factor out the coefficient of x to correctly determine the phase shift c.<br>
After doing that, your function is<br>
{{{3*sin(2(x-pi/2))+0}}}<br>
The amplitude is a=3
The period is 2pi/b = 2pi/2 = pi
The phase shift is c = pi/2
The vertical shift is d = 0<br>
As for key points, perhaps the best place to start -- given a sine function with a phase shift of pi/2, and knowing the basic behavior of the sine function -- is at (pi/2,0).  At that point, the function value is 0 and increasing.<br>
Then, with a period of pi (so a half period of pi/2) the function will be 0 and decreasing at x=pi: (pi,0); and it will be again 0 and increasing at x=3pi/2: (3pi/2,0).<br>
Next, halfway between x=pi/2 (function value 0 and increasing) and x=pi (function value 0 and decreasing) the function will have a maximum: (3pi/4,3); and halfway between x=pi (function value 0 and decreasing) and x=3pi/2 (function value 0 and increasing) the function will have a minimum: (5pi/4,-3).<br>
You should be able to see all of those points on the graph shown.<br>
Finally, with a period of pi, you can find other key points knowing that if you move any multiple of the period pi from any of the above points you will get another point with the same function value.