Question

How do you solve this on the interval of [0,2pi)

Answer 1

Given:

`\tan 3x=1,\lbrack0,2\pi)`

To find the value of x:

Solving we get,

`\begin{gathered} \tan (3x)=1 \\ 3x=(\pi)/(4),(5\pi)/(4),(9\pi)/(4),(13\pi)/(4),(17\pi)/(4),(21\pi)/(4) \\ x=(\pi)/(12),(5\pi)/(12),(3\pi)/(4),(13\pi)/(12),(17\pi)/(12),(7\pi)/(4) \end{gathered}`

Hence, the answers are,

`x=(\pi)/(12),(5\pi)/(12),(3\pi)/(4),(13\pi)/(12),(17\pi)/(12),(7\pi)/(4)`