设 $I=\int_{0}^{\frac{\pi}{4}} \ln (\sin x) \mathrm{d} x, J=\int_{0}^{\frac{\pi}{4}} \ln (\cot x) \mathrm{d} x, K=\int_{0}^{\frac{\pi}{4}} \ln (\cos x) \mathrm{d} x$, 则 $I, J, K$ 的大小关系为( )
$\text{A.}$ $I < J < K$.
$\text{B.}$ $I < K < J$.
$\text{C.}$ $J < I < K$.
$\text{D.}$ $K < J < I$.