# How to find the value of x where 0<=x<=360^@ for csc x= 2.5151?

Jun 2, 2015

If csc(x) = 2.5151#

Since $\sin \left(x\right) = \frac{1}{\csc} \left(x\right)$

$\sin \left(x\right) = \frac{1}{2.5151}$

$x = \arcsin \left(\frac{1}{2.5151}\right) = \arcsin \left(0.397599\right)$

$x = {23.42814}^{\circ}$
$\textcolor{w h i t e}{\text{XXXXX}}$ however this is only the "primary" solution

Within the range $0 \le x \le {360}^{\circ}$
$\textcolor{w h i t e}{\text{XXXXX}}$ $\csc \left(\pi - {23.42814}^{\circ}\right)$

$\textcolor{w h i t e}{\text{XXXXX}}$ $\csc \left({156.5719}^{\circ}\right)$

has the same value.