# Thread: Rotations and systems of equatoins

1. ## Rotations and systems of equatoins

I was searching on google and discovered this forum, so I figure you guys could help me understand this.
The question is to rotate x^2-10xy+y^2+1=0 I understand most of the rotating aspect except for finding theta. The step cot 2(theta)=A-C/B. How do I know what quadrant I should be looking in? When I plug in that equation the result is cot 2(theta)=0 But I dont understand how 2(theta)=pi/2 when it could also equal 3pi/2. Help please

2. Originally Posted by deeartist
I was searching on google and discovered this forum, so I figure you guys could help me understand this.
The question is to rotate x^2-10xy+y^2+1=0 I understand most of the rotating aspect except for finding theta. The step cot 2(theta)=A-C/B. How do I know what quadrant I should be looking in? When I plug in that equation the result is cot 2(theta)=0 But I dont understand how 2(theta)=pi/2 when it could also equal 3pi/2. Help please
Have you tried rotating using:
1. pi/4
2. 3pi/4?

What do you notice?

3. Oh so your saying that you can only rotate using the first quadrant?