How do you evaluate tan (-120˚)?

1 Answer
Noah G
Aug 31, 2016

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!

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