Question

Find \(\csc \left(-120^{\circ}\right)\)

Answer 1

We have that
\[
\csc \left(-120^{\circ}\right)=\frac{1}{\sin \left(-120^{\circ}\right)} .
\]
Then
\[
\sin \left(-120^{\circ}\right)=-\sin \left(-120^{\circ}+180^{\circ}\right)=-\sin 60^{\circ}=-\frac{\sqrt{3}}{2}
\]
So
\[
\frac{1}{\sin \left(-120^{\circ}\right)}=-\frac{2}{\sqrt{3}}=-\frac{2 \sqrt{3}}{3}
\]

Final Answer: The final answer is \(-\frac{2 \sqrt{3}}{3}\)