Question

State the number of solutions a quadratic trigonometric equation can have in one cycle.

Answer 1

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.