Given the following​ function,

Question

y=tan(pi-3x)

1)determine the interval for the principal cycle.
(^ Type your answer in interval notation)

2)Then for the principal​ cycle, determine the equations of the vertical​ asymptotes

3)find the coordinates of the center​ point

4) Find the coordinates of the halfway points.

( Direction - if needed type your points as ordered pair)

Thanks in advance. I'm clueless in this question. I have no idea where to begin or what to write.

Answer 1

Well, you know that the principal cycle for tan(x) is from

-π/2 < x < π/2

So, now you have

-π/2 < π-3x < π/2
-3π/2 < -3x < -π/2
π/2 > x > π/6
or, more usually written,
π/6 < x < π/2

But, you want the principal cycle to be near the origin, so shift it left one period (π/3) and you have

-π/6 < x < π/6

Use the same technique to answer the other questions. The graph is at

http://www.wolframalpha.com/input/?i=tan(%CF%80-3x)