The Sound of Trigonometry -- Answers

The result of combining two tones with the same frequency and phase is a louder tone.
10 sin(200 t)
2 sin(205 t) cos(10 t)

The result of combining two tones of different frequencies is a beat.
sin(200 t) + cos(200 t)
sin(200 t) + sin(400 t)
sin(2 pi t) + sin(2 pi t + 0.2 pi)

The result of combining two tones that are just slightly out-of-phase is a very strong signal of the same amplitude and frequency.
sin(2 pi t) + sin(2 pi t + 0.02 pi)

The result of combining two tones that are just slightly out-of-phase is a very strong signal of the same amplitude and frequency.
sin(2 pi t) + sin(2 pi t + 0.5 pi)
sin(2 pi t) + sin(2 pi t + pi)

The result of combining two tones that are 180 degrees out-of-phase is the zero signal.