Most people who can do math know about the trigometric quadrant chart below:
I was given the equation v = Asin(wt) - Bcos(wt), and asked to convert it to v = Rsin(wt + 0) form.
Now I knew that R must equal the root of (A^2 + B^2), and 0 must be tan^-1(B/A).
However, most of you will know that the angle can be the calculated value above, or the above value + pi. What I overlooked was that a positive sin and negative cos in the initial equation does not mean the angle is in the second quadrant.
v = Asin(wt) - Bcos(wt) can be written as cos(wt).sin(wt) - sin(wt).cos(wt), so A must equal cos(wt), and B must equal -sin(wt).
tan^-1(B/A) can therfore be written as tan^-1(-sin(wt)/cos(wt).
This means that the sin value is infact negative and cos value is positive, placing the angle in the 4th quadrant.
There goes 15 marks :-(.
