Recall your unit circle, or the graph of $f(x) = \operatorname{sin}x$.
Since reference point: $\operatorname{sin}\frac{\pi}{3}=\frac{\sqrt{3}}{2}$, $\operatorname{sin}\frac{5\pi}{3}$ will equal EITHER $\frac{\sqrt{3}}{2}$ or $-\frac{\sqrt{3}}{2}$.
Which one?

$\text{tan}x=\frac{\text{sin}x}{\text{cos}x}$
$\text{tan}\frac{7\pi }{6}=\frac{\text{sin}\frac{7\pi }{6}}{\text{cos}\frac{7\pi }{6}}= \underline{ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$
Now simplify!

$\text{sec}x=\frac{1}{\text{cos}x}$
$\text{sec}\frac{5\pi }{4}=\frac{1}{\text{cos}\frac{5\pi }{4}}= \underline{ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$
Now simplify!

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

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