I am looking for the angle needed to rotate the conic to eliminate the xy-term but the angle I find is negative and I need the counter-clockwise angle of rotation to satisfy 0 < theta < 90 degrees. Where am I going wrong? Or what else do I need to know? Thank you for your help. I have this equation of a conic and I am supposed to find only the angle of rotation with this formula: cot 2(theta) = A - C / B The equation I am using is this: 153x^2 - 192 xy + 97y^2 - 30x -40y - 200 = 0 I then solve for theta plugging these A = 153 , B = -192 , C = 97 into cot 2(theta) = A - C / B I get this equation: cot 2(theta) = -56/192 Let theta = 2*theta Then : cot theta = -56/192 I take the inverse tangent to find 2*theta and then solve for theta like this: arctan ( 192/-56) = -73.7398 degrees Remember I let theta = 2*theta -73.7398 = 2*theta theta = -37 degrees. Is there a way for -37 degrees to satisfy the original question?