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1. Why do we have to use cos? why not sin? wouldnt sine be better so that amplitude starts at zero also? using cos must make things easier, but i dont see why?

2. Is "width" the distance between any two peaks or troughs of the wave? Is this the same as frequency of wave? (if its now, then what is the correct term for width?)

3. doesnt A gradually decrease over time ( this is obvious from intuition) and if so, then why are the waveforms always drawn with uniform amplitude? (is this just an idealized wave (no friction or damping)? AKA: SIMPLE harmonic motion?

4 how do we differentiate between small greek letters and big? for eg, delta looks totally different when small vs big, so what do we say "small delta" or "capital delta" or what? seems confusing..

thanks for any help