Cosecant of Angle plus Full Angle
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Theorem
- $\csc \left({x + 2 \pi}\right) = \csc x$
Proof
\(\ds \csc \left({x + 2 \pi}\right)\) | \(=\) | \(\ds \frac 1 {\sin \left({x + 2 \pi}\right)}\) | Cosecant is Reciprocal of Sine | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac 1 {\sin x}\) | Sine of Angle plus Straight Angle | |||||||||||
\(\ds \) | \(=\) | \(\ds \csc x\) | Cosecant is Reciprocal of Sine |
$\blacksquare$
Also see
- Sine of Angle plus Full Angle
- Cosine of Angle plus Full Angle
- Tangent of Angle plus Full Angle
- Cotangent of Angle plus Full Angle
- Secant 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