How do you solve $tan^2 (x) = 1/3$ from $[0,2pi]$ ?

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Answer 1 · 2015-07-20T03:42:06

Solve $tan^2 x = 1/3$ $(0, 2pi)$

$tan^2 x = 1/3.$ --> $tan x = +- (sqrt3)/3$ . Trig table gives -->

$x = pi/6 + kpi$ and $x = (5pi)/6+ kpi$

Within the interval (0, 2pi), there are 4 answers:

$(pi)/6; and (pi/6 + pi) = (7pi)/6, (5pi)/6; and ((5pi)/6 + pi) = (11pi)/6$

How do you solve tan^2 (x) = 1/3tan^2 (x) = 1/3 from [0,2pi][0,2pi]?