I would like to combine multiple sine waves with differing amplitudes, frequencies and phases into a single curve that I can display as a graph. What formula will I need to create the points for the curve?
You can start out with just
$a_0 \sin(2\pi f_0 t + \phi_0 ) + a_1 \sin(2\pi f_1 t + \phi_1) + \cdots.$
If there are an infinite number of terms, then they might converge into a recognizable waveform that has an easy description as a function such as a square wave or a triangle wave.