Unit circle/Metric by positive angle/Exercise

Let

${}K={\left\{(x,y)\in \mathbb {R} ^{2}\mid x^{2}+y^{2}=1\right\}}\,$

be the unit circle. Show that we can obtain a metric on ${}K$ by defining ${}d(P,Q)$ (${}P,Q\in K$) to be the positive angle at the origin ${}(0,0)$ between the corresponding rays.

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