Explanation
We can convert to given coordinates to polar coordinates using the following formulas:
[tex]\begin{gathered} r=\sqrt{x^2+y^2} \\ \theta=\tan^{-1}(\frac{y}{x}) \end{gathered}[/tex]
Since we have to find the measure of the angle, we use the second formula.
[tex]\begin{gathered} \theta=\tan^{-1}(\frac{y}{x}) \\ \theta=\tan^{-1}(\frac{-\frac{\sqrt{10}}{6}}{\frac{\sqrt{26}}{6}}) \\ \theta=\tan^{-1}(-\frac{\sqrt{10}}{\sqrt{26}}) \end{gathered}[/tex]
Now, we calculate csc(θ).
[tex]\begin{gathered} \csc(\theta)=\csc(\tan^{-1}(-\frac{\sqrt{10}}{\sqrt{26}}) \\ \csc(\theta)=\frac{3\sqrt{10}}{5} \end{gathered}[/tex]Answer
