Question

How do you solve tan^2(theta)-5=0?

Answer 1

\[\tan^{2} x = 5\]
\[\tan x = \pm \sqrt{5}\]
notice there will be 4 solutions for domain of 0<x<360
one for each quadrant
to solve use inverse tan function with calculator
\[x = \tan^{-1} \sqrt{5} \approx 65.91\]
http://www.wolframalpha.com/input/?i=arctan%28sqrt%285%29%29
other solutions can be found using reference angles
180 - 65.91
180 + 65.91
360 - 65.91