Cosecant of 30 Degrees

From ProofWiki
Jump to navigation Jump to search

Theorem

$\csc 30^\circ = \csc \dfrac \pi 6 = 2$

where $\csc$ denotes cosecant.


Proof

\(\displaystyle \csc 30^\circ\) \(=\) \(\displaystyle \frac 1 {\sin 30^\circ}\) Cosecant is Reciprocal of Sine
\(\displaystyle \) \(=\) \(\displaystyle \frac 1 {\frac 1 2}\) Sine of $30^\circ$
\(\displaystyle \) \(=\) \(\displaystyle 2\) multiplying top and bottom by $2$

$\blacksquare$


Sources