The conic section contains an xyterm I intend to perform rot

The conic section contains an xy-term. I intend to perform rotation of axes through some angle Phi to eliminate the xy-term. Find sin phi and cos phi. (You do NOT have to find the angle itself, and without a calculator you probably can\'t find it anyway.) 9x^2 - 24xy + 16y^2 = 100

Solution

tan(2) = B/A-C
= 24/16-9
=24/7
= 73.7 degree
sin=0.96
cos=0.28

16(xcos -ysin)^2 +24(xcos-ysin)(xsin+ycos) +9(xsin+ycos)^2 -73=0

16(x*0.28 - y*0.96)^2 +24(x*0.28 -y*0.96) (x*0.96 +y*0.28) + 9(x*0.28 +y*0.96) -73=0

16(0.078x^2 + 0.92y^2 - 0.54xy) +24(0.27x^2 -0.78xy -0.92xy -0.27y^2) +9(0.078x^2 +0.92y^2 +0.54xy) -73=0

1.248x^2+7.29x^2 +0.702x^2 + 14.72y^2 -7.29y^2 +8.28y^2 -73=0

9.24x^2 + 15.71y^2 =73