Question

arctan((sqrt(3))/3)

Answer 1

\[\tan^{-1} \frac{ \sqrt{3} }{ 3 }\]
This is the same as writing:
\[\tan \theta= \frac{ \sqrt{3} }{ 3 }\]

This is one of your special angles, do you remember the value? :)
It's somewhere in the first quadrant.

Answer 2

since when is arctan the same as tan?

Answer 3

Arctan is the inverse function of the tangent function.
It can be written this way:
\[\tan^{-1} \frac{ \sqrt{3} }{ 3 }=\theta\]

When you take the inverse of this, it means you SWAP the terms
So the sqrt term, and the (theta) will switch places.
And then you change Arctan to Tan.

I know it's a lil tricky to understand :C

Answer 4

so once you flip it then what

Answer 5

Then you're suppose to remember which angle has a tangent of this particular value. It's a special angle :)
it's one of these 5 values.
\[0, \frac{ \pi }{ 6 }, \frac{ \pi }{ 4 }, \frac{ \pi }{ 3 }, \frac{ \pi }{ 2 }\]

Have any idea which one it is? :)