TRIGONOMETRY

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?

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  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

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

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