Answer
$1.3634$ radians
Work Step by Step
RECALL:
$\csc{\theta}=\dfrac{1}{\sin{\theta}}$ and $\sin{\theta}=\dfrac{1}{\csc{\theta}}$
With $\csc{s}=1.0219$, then $\sin{s}=\dfrac{1}{1.0219}$
To find $s$, use the inverse sine function of a calculator in radian mode, then round-off the answer to four decimal places to obtain:
$s=\sin^{-1}{(\frac{1}{1.0219})} \approx 1.3634$
The angle must be within the interval $[0, \frac{\pi}{2}]$,
Noe that $\frac{\pi}{2}\approx 1.5708$.
Thus, the $s-1.3634$ is within the required interval.
