Sinusoids represented by Phasors

[salman213]

1. Find the sinusoids represented by these phasors:
(a) I = -3 + j4 A


3.

well to convert first to polar they got the following

they didnt show their steps:

I = 5 <126.87


then they said

i(t) = 5 cos(wt + 126.87)

What I don't get is the fact that how they got 126.87

to get 5 i just take 3 and 4 sum their squares and take the square root.

to find the angle i would do tan-1(y/x) = tan-1(4/-3)=-53.13

ok since its tangent you may say u can add 180 and it is the same answer which is what they did -53.13 +180=126.87

but my question is WHY. why do they add the 180 if its the same thing. Whats the use. I would just leave my final answer as

i(t) = 5cos(wt - 53.13)

why add 180?

 

[Defennder]

It's easily seen if you sketch the Argand diagram for -3+j4. Remember that the angle you want is measured from the x-axis on the right to the complex number "vector". And that is given by 180 - 53.13.