Question

How do you evaluate `tan(-30)`?

Answer 1

`tan(-30°) = tan 330° = (-1)/sqrt3 = -1/sqrt3`

Explanation:

An angle of 30° is found is a right-angled triangle with sides in the ratio : `1 : 2 : sqrt3`

`Tan 30° = "opp"/"adj" = 1/sqrt3`

However, an angle of `-30°` lies in the 4th quadrant. The opposite side (y value) is negative, which causes tan values in the 4th quadrant to be negative.

(tan -30° = tan 330°)
Therefore `tan(-30°) = (-1)/sqrt3 = -1/sqrt3`