I am studying for a Bachelors in electrical engineering and have a question regarding phasors.
I have been presented with the question:
Find \$V_s\$ for \$V_1 + V_2\$ where
\$V_1 = \sqrt{2} \cdot 20\cdot cos(\omega t – 45)\$
\$V_2 = \sqrt{2} \cdot 10\cdot sin(\omega t + 60)\$
I can get the answer:
\$V_s = \sqrt{2} \cdot 29.77\cdot cos(\omega t – 40.01)\$
I'm not asking the question as a homework cheat! What I don't understand is:
- Why the second phasor is been expressed as a sin function.
- Why do I have to subtract 90 degrees from the angle to resolve the sin function to something workable in rectangular form?
Can anyone tell me why this is the case or point me to a good link that explains why?
Best Answer
The only difference between sine and cosine is a 90 degree phase shift. So you can very easily rewrite that sine as a cosine, all you need to do is adjust the phase appropriately.
$$ \sin(\theta) = \cos\left(\theta - \frac{\pi}{2}\right) $$
However, I will also note that usually omega is an angular frequency measured in radians instead of degrees, so make sure to keep your units consistent!