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Math Help - Basic trig

  1. #1
    Junior Member
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    Basic trig

    Need to find all solutions of this

    Tan^2 x = 1

    Book says {\pi\over 4} + {\pi\over 2}N

    But its Tan x = 1 and Tan x = -1

    So shouldnt the reference angle ( \pi\over 4) be in every quadrant?
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  2. #2
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    The question implies you need to find what angles will give a positive solution for x. Only the 1st and 3rd quadrants have a positive answer for x so you need to find these.

    Using the symmerty identities (keeping in mind that tan has the preiod of \pi ) the solutions for one revolution of the unit circle will be

    x= \frac{\pi}{4},\frac{\pi}{2}+\frac{\pi}{4}

    All solutions are found then by mulitplying through these soultions into every other revolution of the circle.

    So x= \frac{(2k+1)\pi}{4},k=0,1,2,\dots
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