# Thread: trig equation involving tan

1. ## trig equation involving tan

Hello, I am looking at this trig equation: tan^2(3x) = 1 (for values of x greater than or equal to zero and less than or equal to 2pi)
I can understand how to solve it almost right to the end.
I can get to the point where I have tan3x=1 and tan3x = -1. I then get +- 45 degrees. I know I need to divide that by 3, so I end up with 15 degrees.
I know the final answer is:
+-pi/12 + pi/3(k)
But I dont understand this answer.
The problem I am having is plotting those points on a tan graph.
Could someone please tell me the exact values that the answer above represents and where they sit on the tan graph.
Then I can visualize it and understand better.

Thanks kindly for any help.

2. ## Re: trig equation involving tan

15 degree is the same as pi/12, then you are just adding the period of the function for repeated solutions.

3. ## Re: trig equation involving tan

thanks. I am still trying to understand how the correlates with the answer "+-pi/12 + pi/3(k)"
I see the pi/12 = 15 degree, but then what about the last part "+pi/3(k). Isnt that adding 60 degrees to each unit of 15 degree ? Should'nt it be + 180 degrees (pi) ?

Thanks for clarification.

4. ## Re: trig equation involving tan

$\displaystyle \tan x$ has a period of $\displaystyle \pi$

$\displaystyle \tan nx$ has a period of $\displaystyle \frac{\pi}{n}$

5. ## Re: trig equation involving tan

Moved thread to Trig.