What is the angle between two clock hands at 5:51?
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\(\omega_{small} =2\pi/12h\\ \alpha_{small}=t\cdot \omega_{small}=(5+\frac{51}{60})h\cdot\frac{\pi}{6h}\)
\(\alpha_{small}=\frac{5+\frac{51}{60}}{6}\pi\)
\(\alpha_{small}=0.975\pi\)
\(\omega_{large} =2\pi/60min\\ \alpha_{large}=51min\cdot \frac{\pi}{30min}\)
\(\alpha_{large}=1.7\pi\)
\(\Delta\alpha=(1.7-0.975)\cdot\pi\\ \Delta\alpha=0.725\cdot\pi\cdot \frac{180\ deg}{\pi}\)
\(\Delta\alpha=130.5\ deg\)
The angle between two clock hands at 5:51 is 130.5 degrees.
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