Hi
There are many references to this on the net
The main reason we use a sine wave in ac circuits is due to the behaviour of a generator which generates alternating current
If you plot voltage output from a generator according to time you will derive a graph which is sinusoidal in shape and has a direct relation with degrees and radians making up a complete circle.
Or one cycle or 360 degrees or 2 pi radians the units of angular measurement
For a better and more complete understanding of the subject refer to this link below
http://www.allaboutcircuits.com/vol_2/chpt_1/2.html Or
If. You use google or a similar search engine which takes a little practice
Can be a little challenging at times would you believe there are some more thorough explanations to this subject as well
I also suggest further studies in mathematics which if you google again, does mean a little bit of effort, You can gain more understanding by looking up the following
The vertical and horizontal projections of a rotating line
The measurement of Angles in degrees
The definition of the Six Tigonometric Functions
Graphical Representation of the properties of the function Y = Sin (pheta )
or
if you can manage to download a file please see link below