State the number of solutions a quadratic trigonometric equation can have in one cycle.
Since a quadratic can two solutions, and a trig function can two solutions per period, I expect that 4 solutions is as many as you can have.
For example,
sin^2(x) = 1/4
has 4 solutions in one period.
sin^2(x) = 2
has none,
sin^2(x) = 1
has two
Maybe you can find some with an odd number of solutions. For example,
tan^2(x)+tan(x) + 1/4
has one solution
Haven't figured out one with 3 solutions, but I'm sure there's one out there.