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Thread: Basic trig

  1. #1
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    Basic trig

    Need to find all solutions of this

    $\displaystyle Tan^2 x = 1$

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

    But its $\displaystyle Tan x = 1$ and $\displaystyle Tan x = -1$

    So shouldnt the reference angle ($\displaystyle \pi\over 4$) 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 $\displaystyle \pi$ ) the solutions for one revolution of the unit circle will be

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

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

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