means the amplitude, that is, the maximum 'height and depth' of the curve.
You could say that is a transformation from , and the codomain of is
on the same set of axes plot the graphs of y = sin alpha, y = 2sin alpha, y = 3 sin alpha. what can you deduce about the relationship between the curves y = sin alpha and y = k sin alpha?
well from the graph (from a graphic calculator btw) the result is pretty obvious, ijsut dont know the appropriate term to describe it. increase in y, what? some specific transformation?