u(t)=A(t)cos(ω0*t+θ)
AM modulation -change A(t) , θ=const
FM,ΦM - change Θ, A(t)=const
If you need some advanced modulation techniques, you will have to change both amplitude and phase. Standard analyzis with polar Amplitude and angle is not so suitable.
It is much easier to analyze signal by decomposing it into I/Q components (rectangular projections of polar plot).
You can make I/Q components modulating it with cos and sin wave.
On this are based digital modulation techniques.
Acosθcosω0-Asinθsinω0 = I*cosw0-Q*sinw0
I=Acosθ inphase
Q=Asinθ quadrature