The Purplemath Forums

by **AmySaunders** on Fri Jul 09, 2010 7:44 pm

This is my problem and I can not figure it out!!!:
Arctan[tan(7pi/6)]
I have tried to use the reference triangles but no matter what I do, I always come out with the answer: 7pi/6. The answer book, however, says that the answer is pi/6. Any and all help will be appreciated!!

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by **Martingale** on Fri Jul 09, 2010 9:10 pm

AmySaunders wrote:This is my problem and I can not figure it out!!!:
Arctan[tan(7pi/6)]
I have tried to use the reference triangles but no matter what I do, I always come out with the answer: 7pi/6. The answer book, however, says that the answer is pi/6. Any and all help will be appreciated!!

$\frac{7\pi}{6}$ can't be an answer since $\arctan{x}$ is always between $\pm\frac{\pi}{2}$

by **Martingale** on Fri Jul 09, 2010 9:36 pm

AmySaunders wrote:Any and all help will be appreciated!!

remember that tan is pi periodic.

so $\tan\left(\frac{7\pi}{6}\right)=\tan\left(\frac{\pi}{6}\right)$

by **AmySaunders** on Mon Jul 12, 2010 10:15 pm

I'm sorry. I still don't understand? Is there a lesson on here you could refer me to? What does pi periodic mean?

by **Martingale** on Mon Jul 12, 2010 11:22 pm

AmySaunders wrote:What does pi periodic mean?

http://www.wolframalpha.com/input/?i=graph+tan%28x%29

notice how the graph repeats..it does this very pi units

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