Question

How do you find the exact value of `tan^-1 (-1/sqrt3)`?

Answer 1

`color(indigo)(theta = pi n - (pi/6)` with `color(purple)(n in ZZ`

Explanation:

Let `theta = tan ^ -1 (-1/sqrt3)`

`tan theta = tan ( tan^ -1 (-1/ sqrt3)) = -(1/sqrt3)`

()

()

From the above tables,
`tan (pi - (pi/6)) = tan -(pi/6) = -(1/ sqrt3)`

Generalising the same,

`color(indigo)(theta = pi n - (pi/6)` with `color(purple)(n in ZZ`