Question

How do you evaluate `tan^-1(-(sqrt3)/3)`?

Answer 1

`-pi/6`

Explanation:

Let `tan^-1(-sqrt3/3)= A :. tanA=(-sqrt3/3); tan(-pi/6)=-sqrt3/3 :.A= -pi/6`.The range of `tan^-1x` is `(-pi/2,pi/2)`
`:.tan^-1(-sqrt3/3)= -pi/6` since `tan(-pi/6)=-sqrt3/3 and -pi/6 in (-pi/2,pi/2)`[Ans]