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