Why we use most of the time cos function for representing signal ?
There is no specific answer to a generic question like this. For each case it may be more convenient to represent in one form or another; The cosine has the advantage of being an operator that at zero angle has its maximum amplitude. Another point is that in general the real part of a complex variable are projected at X axis by cosines and the imaginary part projected at Y axis by sines. In short, there is not an exact answer to the question as posed.
It's human nature for us to think of zero as a starting point. And it so happens that the sine of 0 deg is zero (whereas the cosine of 0 is 1). 'Sine' is also quicker to pronounce.
So whenever we discuss that shape of curve, or a graph of the curve, or refer to it in concept, it's easy to call it a 'sine'.