Explain how the graph of y = a sin (bx + c) changes for different values a, b, and c?

You could use wolfram and set some values to get a graphical concept. Doing so manually with a calculator is a little tedious but also good during an exam.

A = Larger or smaller oscillations of the sine, depending on magnitude. Sign flips.
B = Makes the waves narrower or wider, depending on magnitude. Sign flips.
C = Shifts the waves forwards or backwards, depending on sign & magnitude.