To draw the basic period of ANY graph of 
an equation of either the form

y = Asin(Bx)  or  y = Acos(Bx), 

ALWAYS begin with this: 



Since our graph is of y = 3sin(2x), A=3 and B=2, we calculate

|A|=3, -|A|=-3, , , , .

Therefore we begin with this:

   

Next we decide which of the 4 types of graphs we have:

1. All graphs of the form y = Asin(Bx) where
A is POSITIVE and B is positive look like this:



2. All graphs of the form y = Asin(Bx) where
A is NEGATIVE and B is positive look like this:



3. All graphs of the form y = Acos(Bx) where
A is POSITIVE and B is positive look like this:



4. All graphs of the form y = Acos(Bx) where
A is NEGATIVE and B is positive look like this:



Our graph is of y= 3sin(2x). which is of the 
form y = Asin(Bx) where A is POSITIVE and B is positive,
our graph is type 1 above, so the answer is:

 


However we should realize that this graph and all sine and cosine
graphs are not just of one period, as we have drawn here, but they
all continue indefinitely forever both to the left and right, like this:



Edwin