Question

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

Answer 1

`theta = 120° + 180n`

Explanation:

We can read `sqrt3` as `sqrt3/1` because tan is the ratio of two sides. The special triangle which has these sides is a right-angled triangle with sides in the ratio `1 : 2 : sqrt3` and angles of 30° and 60°.

`tan 60° = sqrt3/1`

However we are dealing with a negative `sqrt3`

From `0° to 360°` Tan values are negative in the second and fourth quadrants.

`theta = 180°-60° = 120°" or "theta = 360-60 = 300°`

Any angle from `120°` which is a rotation through 180° will be such that `Tan theta = -sqrt3`

Hence `theta = 120° + 180n`