-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:
[tex] \frac{ \frac{ \sqrt{3} }{2} }{ \frac{-1}{2} } = \frac{ \sqrt{3} }{2}* -\frac{2}{1} [/tex]
Simplify, and you get:
[tex] -\frac{2 \sqrt{3} }{2} = - \sqrt{3} [/tex]
And, so, tan(-2π/3) = -√3
