Understanding Phasor Relationships in RC Circuits

[Physics_5]

I understand that the voltage phasor for a resistor is in phase with the current phasor in a simple ac circuit consisting of only an AC voltage source and the resistor.

I understand that the voltage phasor for a capacitor is pi/2 radians behind the current phasor for an AC circuit consisting of only an AC voltage source and a capacitor.

When an RC circuit consisting of a resistor and capacitor in series is analyzed, I don't understand how the above still holds. Both proofs were based on the fact that the voltage across each circuit element varies by E = E0*cos(wt), but now the sum of the voltages across each element vary by this NOT each individual voltage.

I feel like this is a pure assumption. Here are the links to the book proof. I have a problem with the second picture of the phasor diagrams.
http://imgur.com/wmjzJ6C
http://imgur.com/aeh1ESb

 

[Valerie Park]

The proof does not explain why the voltage phasor for the resistor is still in phase with the current phasor and why the voltage phasor for the capacitor is still pi/2 radians behind the current phasor. It simply states that this is the case. I understand that the algebraic equations used to solve for circuit element parameters yield the same result, but I don't understand why the voltage phasors for each element are still in the same position relative to the current phasor.