已知 $a=\log _9 6, b=\sqrt{14}-3, c=\sin 50^{\circ}$, 则
$ \text{A.} $ $c < b < a$
$ \text{B.} $ $b < c < a$
$ \text{C.} $ $b < a < c$
$ \text{D.} $ $a < b < c$
【答案】 B
【解析】
$\sin 3 x=3 \sin x-4 \sin ^3 x, f(t)=3 t-4 t^3, \frac{1}{2} < t < 1$.
$$
\begin{aligned}
& \therefore f^{\prime}(t)=3(1-2 t)(1+2 t) < 0, f(t) \text { 递姷 } \\
& \text { 又: } f\left(\frac{4}{5}\right)=\frac{44}{125} < f\left(\sin 50^{\circ}\right)=\sin 150^{\circ}=\frac{1}{2} < \frac{9}{16}=f\left(\frac{3}{4}\right) . \\
& \therefore b=\sqrt{14}-3 < \frac{3}{4} < c=\sin 50^{\circ} < \frac{4}{5} < \log _9 6=a .
\end{aligned}
$$