Question 23
For $0^\circ\lt \alpha\lt 180^\circ$, the quadratic equation
$$(3\sin\alpha)x^2-(4\cos\alpha)x+2=0$$
has a real root. Find the exact range of $\sin\alpha$.
Editorial normalization: the source prints a double-less-than glyph in its angle bounds and options. Use the strict angle bounds shown here and allow repeated real roots. In every displayed option below, the lower bound is strict and the upper bound inclusive. Choose the exact range, not merely an interval containing it. The original options are also reproduced for comparison.
Original source image, preserving the printed mathematical labels and any disclosed source discrepancy.
$$(3\sin\alpha)x^2-(4\cos\alpha)x+2=0$$
has a real root. Find the exact range of $\sin\alpha$.
Editorial normalization: the source prints a double-less-than glyph in its angle bounds and options. Use the strict angle bounds shown here and allow repeated real roots. In every displayed option below, the lower bound is strict and the upper bound inclusive. Choose the exact range, not merely an interval containing it. The original options are also reproduced for comparison.
Original source image, preserving the printed mathematical labels and any disclosed source discrepancy.