Find to the nearest degree the solution set of 4 cos^2 x =9 sin x +6

Question

Its over the domain {x| 0 < x <360}

Answer 1

cos^2(x)=1-sin^2(x), so we can write: 4-4sin^2(x)=9sin(x)+6; 4sin^2(x)+9sin(x)+2=0. (4sin(x)+1)(sin(x)+2)=0.

Therefore sin(x)=-1/4 is the only valid solution. Therefore x=194.48, 345.52 degrees, or 194, 346 to the nearest degree.