Respuesta :

cerverusdante
To solve this we are going to use the unitary circle and the fact that [tex]tan \alpha = \frac{sin \alpha }{cos \alpha } [/tex]

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

Since [tex]tan \alpha = \frac{sin \alpha }{cos \alpha } [/tex], [tex]tan\frac{5 \pi }{3}= \frac{\frac{- \sqrt{3} }{2}}{\frac{1}{2} } [/tex]
[tex]tan\frac{5 \pi }{3}=- \sqrt{3} [/tex]

We can conclude that [tex]tan\frac{5 \pi }{3}=- \sqrt{3} [/tex].
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aencabo
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