Question

How do you evaluate `tan ((2pi)/3)`?

Answer 1

`tan((2pi)/3)=-sqrt3`

Explanation:

`tan((2pi)/3)`

Recall the identity `tantheta=sintheta/costheta`

According to the unit circle,

`sin((2pi)/3)=sqrt3/2` and `cos((2pi)/3)=-1/2`

`tan((2pi)/3) =frac{sin((2pi)/3)}{cos((2pi)/3)}=frac(sqrt3/2)(-1/2)`

`=sqrt3/2 * -2/1=sqrt3/cancel2 * -cancel2/1=-sqrt3`