Question

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

Answer 1

`pi/6`

Explanation:

Another way of asking this question is: "the tangent of what angle gives me `sqrt3/3`?"

We know that `" "tan(pi/6)=sqrt3/3`.

So then, `" "" "tan^-1(sqrt3/3)=pi/6`

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Note that even though tangent is positive in the third quadrant, and that the tangent of an infinite amount of coterminal angles is `sqrt3/3`, we need to observe that the range of `tan^-1(x)` is `(-pi/2,pi/2)`, so only `pi/6` is a valid answer within this range.