Step-by-step explanation:
If the question is like this,
[tex] \tan( \frac{\pi}{3}x - 3 ) = 0[/tex]
We take the arc tan of both sides.
[tex] \tan( - 1) ( \tan( \frac{\pi}{3}x - 3 ) = \tan {}^{ - 1} ( {}^{ }0 ) [/tex]
[tex] \frac{\pi}{3} x - 3 = 0[/tex]
[tex] \frac{\pi}{3} x = 3[/tex]
[tex] = \frac{9}{\pi} [/tex]
Since the period of a tan function, is pi, we divide pi by pi/3 since pi/3is the coeffeicent of the x variable
[tex] \frac{\pi}{ \frac{\pi}{3} } = 3[/tex]
So the answer is
[tex] \frac{9}{\pi} + 3n[/tex]
If this the question,
[tex] \tan( \frac{\pi}{3} x) = 3[/tex]
[tex] \frac{\pi}{3} x = 1.249[/tex]
[tex]x = \frac{3.747}{\pi} [/tex]
The period is once again 3 so we have
[tex] \frac{3.747}{\pi} + 3n[/tex]
where n is a interger.
