Cosine of Full Angle

Theorem

$\cos 360 \degrees = \cos 2 \pi = 1$

where $\cos$ denotes cosine and $360 \degrees = 2 \pi$ is the full angle.

Proof

A direct implementation of Cosine of Multiple of Pi:

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

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

$\cos 2 \pi = \paren {-1}^2 = 1$

$\blacksquare$

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