Sine of Full Angle

Theorem

$\sin 360^\circ = \sin 2 \pi = 0$

where $\sin$ denotes the sine function and $360^\circ = 2 \pi$ is the full angle.


Proof

A direct implementation of Sine of Multiple of Pi:

$\forall n \in \Z: \sin n \pi = 0$

In this case, $n = 2$ and so:

$\sin 2 \pi = 0$

$\blacksquare$


Sources

  • 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles
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