Phasor and time domain help?

Tlx23

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Joined
Apr 24, 2013
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Hello,

Im new here I have two questions both about phasors and time domain functions, not specifically sure what category these fall under I guess you dont really use any 'calculus' in these questions, but I consider them a bit more advanced than regular algebra.

Im given a function g(t)= 2cos(20t-30degrees) +8sin(20t+60degrees) and the question ask's which of the following phasors corresponds to the time domain function?
A. G=5sqrt3 - j5
B. G=5sqrt3 + j5
C. G=5sqrt3 - j3
D. G=-3sqrt3 + j5
E. G=-3sqrt3 + j3

I got the phasors in terms of 2e^j(30) and 8e^-j(30) im pretty sure those are right however Im lost on how to get them into the forms given.

The second question im lost on is: Which of the following is the time domain function that corresponds to the phasor F= 1-jsqrt(3)?
A. f(t)=2cos(wt-60degrees)
B. f(t)=(1+sqrt(3))cos(wt-60degrees)
C. F(t)= 2cos(wt-30degrees)
D. f(t)= (1+sqrt3)cos(wt-30degrees)
E. f(t)= 2cos(wt+30degrees)

for this one I am approaching it as a right triangle with a=1 and b=-jsqrt3 however for the coefficiant in front of the cos im getting 1-jsqrt3 which is in none of the answers, so im probably approaching it wrong.

Any help or insight would be appreciated this is for a Circuits class and my book doesnt explain this very well and my teacher never mentioned it ive been stuck on these for awhile.
Also j=sqrt(-1) or in math imaginary number i and w is actually lowercase omega which stands for the angular frequency. Thanks!
 
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