The problem I'm essentially trying to solve looks like the animation below. Given two sine waves with the same frequency but different phases and amplitudes (here represented as phasors), what is the peak amplitude of their sum across a 360 degree rotation of the phasor.
If my understanding of phasors is right, summing the two phasors on the complex plane at a given instant should produce a phasor that represents the sum of the actual waveforms.