1. Given two points $P(\cos \alpha, \sin \alpha), Q(\cos \beta, \sin \beta)$, then the maximum value of $|P Q|$ is
A. $\sqrt{2}$
B. 2
C. 4
D. Does not exist
1. B Hint: $|P Q|=\sqrt{(\cos \alpha-\cos \beta)^{2}+(\sin \alpha-\sin \beta)^{2}}=\sqrt{2-2 \cos (\alpha-\beta)} \leqslant \sqrt{2+2}=2$. Or use the fact that $P, Q$ are both on the unit circle.