Question

How do you evaluate `arctan((sqrt (3)) /3)`?

Answer 1

`arctan(sqrt(3)/3)= pi/6=30^@`

Explanation:

Note that `sqrt(3)/3 = 1/sqrt(3)`
Here is a standard trigonometric triangle with this ratio for the tan:

Note that by definition the `arctan` function has a range of `[0,pi)`

Answer 2

`arc tan (sqrt3/3)= pi/6 in [0, pi]`. It has two values `pi/6 and (7pi)/6 in [0, 2pi]`. The general value is `npi+pi/6, n=0,+-1,+-2,+-3...`. ,

Explanation:

Thanks to Alan for the timely correction, over my seeing `pi/6 as pi/3`. Now, I am replacing `pi/3` by `pi/6`, everywhere.
`tan (pi/6) = 1/sqrt 3. tan ((7pi)/6)=tan(pi+pi/6)=tan (pi/6)=1/sqrt 3`.

If a is a solution in `[0, 2pi]` for `b = tan a`, then

`arc tan b = npi + a, n=0,+-1,+-2,+-3...`

Here, `b=(3/sqrt 3) = 1/sqrt 3 and a= pi/6 or (7pi)/6`.