remolatg

2021-08-15

Use the fundamental identities to find the value of the trigonometric function
Find $\mathrm{csc}\theta$, given that $\mathrm{sin}\theta =-23$ and $\theta$ is in quadrant 4.

Willie

Given,
We have to find the value of csc using the fundamental identities of trigonometry.
Concept used:
1. $\mathrm{csc}\theta =\frac{1}{\mathrm{sin}\theta }$
2. $\mathrm{csc}\theta$ is positive in 4 quadrant.
Calculation
$\because \mathrm{sin}\theta =-23$
$\therefore \mathrm{csc}\theta =\frac{1}{\mathrm{sin}\theta }=\frac{1}{-23}=-\frac{1}{23}$
But $\mathrm{csc}\theta$ is positive in 4 quadrant.
$⇒\mathrm{csc}\theta =\frac{1}{23}$

Jeffrey Jordon