Cosine of Angle plus Full Angle
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Theorem
- $\map \cos {x + 2 \pi} = \cos x$
Corollary
Let $n \in \Z$ be an integer.
Then:
- $\map \cos {x + 2 n \pi} = \cos x$
Proof
\(\ds \map \cos {x + 2 \pi}\) | \(=\) | \(\ds \cos x \cos 2 \pi - \sin x \sin 2 \pi\) | Cosine of Sum | |||||||||||
\(\ds \) | \(=\) | \(\ds \cos x \cdot 1 - \sin x \cdot 0\) | Cosine of Full Angle and Sine of Full Angle | |||||||||||
\(\ds \) | \(=\) | \(\ds \cos x\) |
$\blacksquare$
Also see
- Sine of Angle plus Full Angle
- Tangent of Angle plus Full Angle
- Cotangent of Angle plus Full Angle
- Secant of Angle plus Full Angle
- Cosecant of Angle plus Full Angle
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Functions of Angles in All Quadrants in terms of those in Quadrant I