phasor question

[dwssatx]

I'm blanking on this. Can anyone break down for me how this fraction was simplified? See attached image. Thank you!

 

[Ryan P.E.]

See 1.1.2 and 1.1.6 from below

http://www.propagation.gatech.edu/ECE3025/opencourse/THT/EmagNotes_Phasors.pdf

Phasor's drop the "w" or frequency part, but you need to remember what it is in case you need to go back to a sinusoidal form which is the case here.

1) represent 359.3cos(wt) as a phasor in polar form: 359.9 angle 0

2) 26.93 angle -68.2 is a phasor already in polar form

3) perform division in polar form, divide the magnitudes (359.3/26.93=13.34) and subtract the angles (0 - -68.2=68.2) to get 13.34 angle 68.2

4) convert the phasor from polar form to sinusoidal form, 13.34cos(wt+68.2)

 

[dwssatx]

thank you!