4. Let $x \in\left(-\frac{1}{2}, 0\right)$, among the following three numbers: $\alpha_{1}=\cos (\sin x \pi), \alpha_{2}=\sin (\cos x \pi), \alpha_{3}=\cos (x+1) \pi$, the size relationship is
(A) $\alpha_{3}<\alpha_{2}<\alpha_{1}$
(B) $\alpha_{1}<\alpha_{3}<\alpha_{2}$
(C) $\alpha_{3}<\alpha_{1}<\alpha_{2}$
(D) $\alpha_{2}<\alpha_{3}<\alpha_{1}$
4. 【Analysis and Solution】Solution 1 Since this is a multiple-choice question, we can use the special value method to solve this problem. Let $x=-\frac{1}{3}$, and calculate the values of several expressions in the question:
$$
\begin{array}{l}
\cos (\sin x \pi)=\cos \left(\frac{1}{2}\right)=\sin \left(\frac{\pi-1}{2}\right), \\
\sin (\cos x \pi)=\sin \left(\frac{\sqrt{3}}{2}\right)\cos k>\sin (\cos k)=\alpha_{2}>0, \alpha_{3}=-\cos k\alpha_{2}>\alpha_{3}$. Choose (A).
$$