Question

What is the value of the expression?

Answer 1

To solve this we are going to use the unitary circle and the fact that $tan \alpha = \frac{sin \alpha }{cos \alpha }$

From our circle we can infer that $sin\frac{5 \pi }{3}= \frac{- \sqrt{3} }{2}$ and $cos\frac{5 \pi }{3}= \frac{1}{2}$.

Since $tan \alpha = \frac{sin \alpha }{cos \alpha }$, $tan\frac{5 \pi }{3}= \frac{\frac{- \sqrt{3} }{2}}{\frac{1}{2} }$
$tan\frac{5 \pi }{3}=- \sqrt{3}$

We can conclude that $tan\frac{5 \pi }{3}=- \sqrt{3}$.

Answer 2

Tan 5pi/3 = -sqrt(3)

I dont know how to explain it, but does it really need to have solution? If not, you can input it in a scientific calculator, and ta-da! 

Hope this helps! Goodluck