Cosecant of Straight Angle
(Redirected from Cosecant of 180 Degrees)
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Theorem
- $\csc 180 \degrees = \csc \pi$ is undefined
where $\csc$ denotes cosecant.
Proof
From Cosecant is Reciprocal of Sine:
- $\csc \theta = \dfrac 1 {\sin \theta}$
From Sine of Straight Angle:
- $\sin \pi = 0$
Thus $\csc \theta$ is undefined at this value.
$\blacksquare$
Also see
- Sine of Straight Angle
- Cosine of Straight Angle
- Tangent of Straight Angle
- Cotangent of Straight Angle
- Secant of Straight Angle
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