Question

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?

Answer 1

by test time you need to know the "standard" angles with easy-to-recall 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

Answer 2

Aah, okay! That's easy enough! That makes total sense. Thanks!