Cosine of Straight Angle

Theorem

$\cos 180 \degrees = \cos \pi = -1$

where $\cos$ denotes cosine.


Proof

A direct implementation of Cosine of Multiple of Pi:

$\forall n \in \Z: \cos n \pi = \paren {-1}^n$

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

$\cos \pi = -1^1 = -1$

$\blacksquare$


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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