The general form for a sin function is;
#y=Asin(Bx + C) +D#
Each constant, #A#, #B#, #C#, and #D# tells us something about the function. #C# and #D# tell us the horizontal and vertical shift of the function. In the case of #y=3sin(2x)# both are zero, so the graph isn't translated up or to the side.
#A# is the amplitude, so #A=3# tells us that the graph is going to fluctuate between #3# and #-3#.
Lastly, #B# is the frequency. #B=2# tells us that there will be #2# full waves between #0# and #2pi#. A more useful number would be the period, #p#.
#p = (2pi)/B = (cancel(2)pi)/cancel(2) = pi#
So we know that the wave is going to repeat every #pi# radians.
A sin wave starts at #0#, goes to #A#, back to #0#, then to #-A#.
