What is the exact value of each of the following trig expressions? 

1. $\sin\left(\frac{5\pi}{3}\right)$

   Hint (a):

   Recall your unit circle, or the graph of $f(x) = \sin x$.

   $\text{Since reference point: sin}\frac{\pi}{3}=\frac{\sqrt{3}}{2},$

   $\text{sin}\frac{5\pi}{3}\text{ will equal EITHER}\frac{\sqrt{3}}{2}\text{ or }-\frac{\sqrt{3}}{2}.$

   Which one?

2. $\tan\left(\frac{7\pi}{6}\right)$

   Hint (b):

   $\text{tan}x=\frac{\text{sin}x}{\text{cos}x}$

   $\text{tan}\frac{7\pi }{6}=\frac{\text{sin}\frac{7\pi }{6}}{\text{cos}\frac{7\pi }{6}}= \underline{ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$

   Now simplify!

3. $\sec\left(\frac{5\pi}{4}\right)$

   Hint (c):

   $\text{sec}x=\frac{1}{\text{cos}x}$

   $\text{sec}\frac{5\pi }{4}=\frac{1}{\text{cos}\frac{5\pi }{4}}= \underline{ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$

   Now simplify!

4. $\csc\left(\pi\right)$

   Hint (d):

   $\text{csc}x=\frac{1}{\text{sin}x}$

   More Help (d):

   Careful! $\sin π = 0$. What does that mean about the reciprocal of $\sin x$.