TRIGONOMETRY
posted by Kate .
Evaluate the expressions:
a) arctan(sqrt(3))
a) Arctan(sqrt(3))
So, I know how to find the answers with a calculator, but how do I find it step by step?

by test time you need to know the "standard" angles with easytorecall trig functions
0,π/6,π/4,π/3,π/2
If you know those angles and their trig ratios, you will recall that
tan π/3 = √3
Now, recall the bit about principal values of inverse trig functions. You restrict the domain so that the range is one continuous period, containing 0, if possible.
π/2 <= Arcsin(x) < π/2
0 <= Arccos(x) <= π
π/2 < Arctan(x) < π/2
...
arctan(√3) = π/3 + 2kπ
Arctan(√3) = π/3 
Aah, okay! That's easy enough! That makes total sense. Thanks!