Cosine of Straight Angle
(Redirected from Cosine of 180 Degrees)
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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
- Sine of Straight Angle
- Tangent of Straight Angle
- Cotangent of Straight Angle
- Secant of Straight Angle
- Cosecant of Straight Angle
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