Cosecant of Right Angle

Theorem

$\csc 90 \degrees = \csc \dfrac \pi 2 = 1$

where $\csc$ denotes cosecant.


Proof

\(\ds \csc 90 \degrees\) \(=\) \(\ds \frac 1 {\sin 90 \degrees}\) Cosecant is Reciprocal of Sine
\(\ds \) \(=\) \(\ds \frac 1 1\) Sine of Right Angle
\(\ds \) \(=\) \(\ds 1\)

$\blacksquare$


Also see


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
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