Question

How do you find the exact value of tan (23pi/6)?

Answer 1

`-1/sqrt3, or, -sqrt3/3`.

Explanation:

`tan(23/6pi)=tan{(24-1)/6pi}=tan{(24/6-1/6)pi}`,

`=tan(4pi-pi/6)`.

Since, `(4pi-pi/6)` lies in the fourth quadrant, where, tan is

-ve, we get,

`tan(23/6pi)=tan(4pi-pi/6)=-tan(pi/6)=-1/sqrt3, or, -sqrt3/3`.