A question about terminology:
I have a simple trigonometric equation in one unknown $\theta$, $$A \cdot \cot(\theta) + B = 0.$$
I want to say that "this equation has either no solution, infinitely many solutions, or unique solution, depending on the values of the parameters $A$ and $B$".
How can this be worded more concisely? Would it be OK to write "the behavior of the equation depends on the values of the parameters $A$ and $B$"? Any better idea?
"The cardinality of the solution set depends on the parameters".