# How do you find the exact value of csc((17pi)/6)

How do you find the exact value of $\mathrm{csc}\left(\frac{17\pi }{6}\right)$?
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Kayleigh Cross
First find the angle coterminal to $\frac{17\pi }{6}$ that falls between 0 and $2\pi$ :
$\frac{17\pi }{6}-2\pi =\frac{5\pi }{6}$. So we know that $\mathrm{csc}\left(\frac{17\pi }{6}\right)=\mathrm{csc}\left(\frac{5\pi }{6}\right)$
$\mathrm{csc}\left(x\right)=\frac{1}{\mathrm{sin}\left(x\right)}$ and we know that $\mathrm{sin}\left(\frac{5\pi }{6}\right)=\frac{1}{2}$ because it's from the Unit Circle.
So:
$\mathrm{csc}\left(\frac{17\pi }{6}\right)=\mathrm{csc}\left(\frac{5\pi }{6}\right)=\frac{1}{\mathrm{sin}\left(\frac{5\pi }{6}\right)}=\frac{1}{\frac{1}{2}}=2$