Question

How do we find `tan(-120^@)`?

Answer 1

`tan (-120^@) = sqrt3`

Explanation:

`tan (-120^@) = tan (-120^@ + 180^@) = tan 60^@`
Consider the right triangle ABC with `2` angles `A = 30^@` and
`B = 60^@`, and with side `AB = a`
We know that in such right triangle,
leg `AC = ((asqrt3)/2)`, and
leg `BC = a/2`
Therefor:
`tan B = tan 60^@ = (AC)/(BC) = ((asqrt3)/2)(2/a) = sqrt3`