How do you find the general solutions for $tan^2 (x) = 1/3$ ?

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Answer 1 · 2015-08-22T23:45:19

Solve $tan^2 x = 1/3$

$tan^2 x = 1/3$ --> $tan x = +- 1/sqrt3 = +- sqrt3/3$

a. $tan x = sqrt3/3$ --> $x = pi/6 + kpi$

b. $tan x = - sqrt3/3$ --> $x = (5pi)/6 + kpi$

Answer 2 · 2015-08-22T23:55:32

$x=npi+-pi/6$

If $tan^2(x) = 1/3$

$rarr tan(x) = +-1/sqrt(3)$

The image below shows the possible configurations:
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How do you find the general solutions for tan^2 (x) = 1/3tan^2 (x) = 1/3?