How do you solve the equation on the interval [0,2pi) for $|tan(t)|=1/sqrt(3)$ ?

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Answer 1 · 2016-06-29T05:57:26

$pi/3, (2pi)/3, (4pi)/3 and (5pi)/3$

$|tan theta|=1/sqrt 3$ is the combined equation for the pair

$tan theta = 1/sqrt 3 and tan theta = -1/sqrt 3$

The principal values of theta are $+-pi/3$ .

The general values are $npi+pi/3, n= 0, +-1, +-2,...$ and

$npi-pi/3, n= 0, +-1, +-2,...$

In $(0, 2pi)$ , the first gives #pi/3 (n=0) and (4pi)/3(n=1).

In $(0, 2pi)$ , the second gives #2pi/3 (n=1) and (5pi)/3(n=21).

How do you solve the equation on the interval [0,2pi) for |tan(t)|=1/sqrt(3)|tan(t)|=1/sqrt(3)?