Question

Evaluate: tan(-120 degrees).

Answer 1

-120° = -2π/3 radians.

Tangent is defined as Opposite/Adjacent or Sine/Cosine in a unit circle. So, if you have memorized the unit circle,

sin(-2π/3) = √3/2
cos(-2π/3) = -1/2

So, tan(-2π/3) would be:
$\frac{ \frac{ \sqrt{3} }{2} }{ \frac{-1}{2} } = \frac{ \sqrt{3} }{2}* -\frac{2}{1}$

Simplify, and you get:
$-\frac{2 \sqrt{3} }{2} = - \sqrt{3}$

And, so, tan(-2π/3) = -√3