Question

What is the value of the expression?

Answer 1

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

Answer 2

To solve this we are going to use the unitary circle and the fact that
`tan \alpha = (sin \alpha )/(cos \alpha )`

From our circle we can infer that
`sin(5 \pi )/(3)= (- √(3) )/(2)` and
`cos(5 \pi )/(3)= (1)/(2)`.

Since
`tan \alpha = (sin \alpha )/(cos \alpha )`,
`tan(5 \pi )/(3)= ((- √(3) )/(2))/((1)/(2) )`

`tan(5 \pi )/(3)=- √(3)`

We can conclude that
`tan(5 \pi )/(3)=- √(3)`.