Cosecant of Angle plus Straight Angle
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Theorem
- $\map \csc {x + \pi} = -\csc x$
Proof
\(\ds \map \csc {x + \pi}\) | \(=\) | \(\ds \frac 1 {\map \sin {x + \pi} }\) | 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 Straight Angle
- Cosine of Angle plus Straight Angle
- Tangent of Angle plus Straight Angle
- Cotangent of Angle plus Straight Angle
- Secant of Angle plus Straight 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