Question

-2sin^2(x)-1cos(x)=-1
Looking for the smallest non-negative solution and the next smallest non-negative solution
Smallest non-negative solution: 0, ?
Next smallest non-negative solution: 360, ?

Answer 1

-2sin^2(x)-cos(x)=-1
-2(1-cos^2(x))-cos(x)=-1
-2+2cos^2(x)-cos(x)=-1
2cos^2(x)-cos(x)-1=0
(cosx-1)(2cosx+1)=0
cosx=1 or cosx=-1/2
x=0,360,720,... or x=120, 240, ...
therefore, Smallest non-negative solution=0
and the next smallest non-negative solution =120