Question

Why is the arctan of equal to pi/6? My teacher says it's pi/6 but is it really that or is it pi/3? Maybe he messed up when providing the answer?

arctan`sqrt3`

Answer 1

I think you are right, it is `pi/3` that produces a tan of `sqrt3`

Explanation:

Tan is equal to `sin/cos`, and for `pi/6`, these values are

`sin(pi/3) = sqrt3/2`

`cos(pi/3)=1/2`

So, `tan(pi/3)=(sqrt3/2)/(1/2) = sqrt3`

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