[tex]csc(\frac{13\pi}{6})=\frac{1}{sin(\frac{13\pi}{6})}[/tex]
The meaning of 13*pi/6 is as if you made 13 complete revolutions around the point pi/6.
therefore, is the same calculate the sin of 13pi/6 than the sin of pi/6.
[tex]\begin{gathered} sin(\frac{\pi}{6})=\frac{1}{2} \\ sin(\frac{13\pi}{6})=\frac{1}{2} \end{gathered}[/tex]
Substituing:
[tex]csc(\frac{13\pi}{6})=\frac{1}{sin(\frac{13\pi}{6})}=\frac{1}{\frac{1}{2}}=2[/tex]
The answer is: csc(13pi/6)=2.
