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

How Do You Solve This On The Interval Of 02pi class=

Sagot :

Given:

[tex]\tan 3x=1,\lbrack0,2\pi)[/tex]

To find the value of x:

Solving we get,

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

Hence, the answers are,

[tex]x=\frac{\pi}{12},\frac{5\pi}{12},\frac{3\pi}{4},\frac{13\pi}{12},\frac{17\pi}{12},\frac{7\pi}{4}[/tex]

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