Question

How do you evaluate `tan (-120˚)`?

Answer 1

`tan(-120˚) = sqrt(3)`

Explanation:

A negative angle, in standard position is drawn in clock-wise direction. A positive angle is drawn in clock-wise.

Since the angles in a unit circle add up to `360˚`, and it's a circle, we can convert a negative angle to a positive angle and vice-versa.

`-120˚ = 360˚ - 120˚ = 240˚`

Now, we can get to work with the evaluation.

The reference angle of `240˚` is `60˚`

By the `1-sqrt(3)-2` special triangle, `tan60˚ = sqrt(3)/1 = sqrt(3)`. `240˚` is in quadrant `III`, so tangent is positive (our answer will be positive). Hence, `tan(-120˚) = tan(240˚) = sqrt(3)`

Hopefully this helps!