Sine of Straight Angle

Theorem

$\sin 180 \degrees = \sin \pi = 0$

where:

$\sin$ denotes the sine function
$180 \degrees = \pi$ is the straight angle.


Proof

A direct implementation of Sine of Multiple of Pi:

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

In this case, $n = 1$ and so:

$\sin \pi = 0$

$\blacksquare$


Also see


Sources

  • 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Special angles
  • 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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