Cosecant of 60 Degrees

Theorem

$\csc 60^\circ = \csc \dfrac \pi 3 = \dfrac {2 \sqrt 3} 3$

where $\csc$ denotes cosecant.

Proof

\(\ds \csc 60^\circ\)

\(=\)

\(\ds \frac 1 {\sin 60^\circ}\)

Cosecant is Reciprocal of Sine

\(\ds \)

\(=\)

\(\ds \frac 1 {\frac {\sqrt 3} 2}\)

Sine of 60 Degrees

\(\ds \)

\(=\)

\(\ds \frac {2 \sqrt 3} 3\)

multiplying top and bottom by $2 \sqrt 3$

$\blacksquare$

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