Question

How do you evaluate the arctan of sqrt3/3?

Answer 1

One approach: Ask yourself: Which angle has a tanget of \[\frac{ \sqrt{3} }{ 2 }?\]

Answer 2

The tangent is defined as \[\tan x = \frac{ opposite }{ adjacent }\]

Answer 3

where "opposite" refers to the length of the side of the triangle opposite angle x,
and "adjacent" refs. to the length of the side adjacent to x.

Answer 4

sorry for the typos in my first response.

Ask yourself: Which angle has tangent equal to \[\frac{ \sqrt{3} }{ 3 }?\]

Answer 5

Note that this is the same as \[\frac{ 1 }{ \sqrt{3} }\]

Answer 6

Here, the angle x is very frequently seen, and so you should know its sine and cosine by heart. Knowing the sine and cosine, you can find the tangent also, by using the definition of "tangent."