Sine is Reciprocal of Cosecant

From ProofWiki
Jump to navigation Jump to search

Theorem

Let $\theta$ be an angle such that $\sin \theta \ne 0$.

Then:

$\sin \theta = \dfrac 1 {\csc \theta}$

where $\sin$ denotes the sine function and $\csc$ denotes the cosecant function.


Proof

\(\ds \frac 1 {\sin \theta}\) \(=\) \(\ds \csc \theta\) Cosecant is Reciprocal of Sine
\(\ds \leadsto \ \ \) \(\ds \sin \theta\) \(=\) \(\ds \frac 1 {\csc \theta}\)

$\blacksquare$


Also see