Question

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

Answer 1

This can either equal `240˚` or `60˚`.

Explanation:

First of all, you need to find the quadrants where tangent is positive. You can remember the signs of the trigonometric functions in the quadrants using the following rule.

Tangent is positive in quadrants `I` and `III`.

Now take the special triangle possessing sides of length `1-sqrt(3)-2`.

`tantheta = "opposite"/"adjacent"`, so the opposite side must measure `sqrt(3)` and the adjacent side must measure `1`, because `tantheta = sqrt(3)`.

In the special triangle, the angle of `60˚` is opposite the side measuring `sqrt(3)`, so we know the reference angle of `theta` is `60^@`.

We mentioned earlier that tangent is positive in quadrants `I` and `III`, so `theta = 60˚ and 180˚ + 60˚ =240˚`

Hopefully this helps!