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

Question

Its over the domain {x| 0 greater than or equal to x <360}

Answer 1

4cos²(x)=9sin(x)+6,

4-4sin²(x)=9sin(x)+6,

4sin²(x)+9sin(x)+2=0=(4sin(x)+1)(sin(x)+2). Since sine is confined to the interval [-1,1], the only acceptable solution is sin(x)=-¼, and x=-14.4775° or -14° to the nearest degree.

-14°=360-14=346° and 194° are solutions for 0≤x≤360°.