As the amplitude is 3 and there is no vertical translation or dilation parallel to the x-axis, the maximums would be at and the minimums would be at (where is an integer).
As for the zeros, there would also be infinitely many, since there is no domain specified.
If the domain were (i.e. one cycle of this particular function) the zeros would be at and
There's a good guide to basic trig graphs and functions here: http://www.purplemath.com/modules/triggrph.htm