Question

What is the reciprocal of $\sin e$?

Answer 1

Trigonomteric ratios:

In a right-angled triangle, the $\sin \left(\theta \right)$ is given as the ratio between the opposite side and the hypotenuse.

The reciprocal of sine is cosecant. $\mathrm{cosec}\left(\theta \right)$ is given as the ratio between the hypotenuse and the opposite side.

$\mathbf{sin}\left(\theta \right)\mathbf{=}\frac{\mathbf{opposite}\mathbf{}\mathbf{side}}{\mathbf{hypotenuse}}$

$\mathbf{cosec}\left(\theta \right)\mathbf{=}\frac{\mathbf{hypotenuse}}{\mathbf{opposite}\mathbf{}\mathbf{side}}$

Hence,the reciprocal of $\mathbf{sine}$ is $\mathbf{cosine}$.