The trigonometric function we need to evaluate is:
[tex]\csc\theta[/tex]
This function is given by:
[tex]\csc\theta=\frac{hypotenuse}{opposite}[/tex]
In the unit circle, graphically these measures are given by:
Then, the cosecant will be undefined when the opposite side (y-value) is equal to zero, so let's check the given angles:
[tex]\begin{gathered} \csc0=\frac{1}{0}=undefined \\ \\ \csc90=\frac{1}{1}=1 \\ \\ \csc270=\frac{1}{-1}=-1 \end{gathered}[/tex]
And we can't find the exact value of csc 315, but with a little help from the unit circle, we can observe that the opposite side measures a value different than 0:
So, the answer is 0°.
