The angle is in the third quadrant, therefore we can conclude that:
[tex]\begin{gathered} tan(\theta)=-1 \\ _{\text{ }}where: \\ \theta=-180-45=-225 \\ or \\ \theta=-90-45=-135 \end{gathered}[/tex]
So:
[tex]csc(\theta)=\frac{1}{sin(\theta)}=\frac{1}{sin(-225)}=\sqrt{2}[/tex]
Answer:
[tex]\sqrt{2}[/tex]
