Sine of Full Angle
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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