Arctangent confusing to me

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
AmySaunders
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Joined: Thu Aug 20, 2009 6:27 pm
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Arctangent confusing to me

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!!

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
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Re: Arctangent confusing to me

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 $\pm\frac{\pi}{2}$

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
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Re: Arctangent confusing to me

Any and all help will be appreciated!!
remember that tan is pi periodic.

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

AmySaunders
Posts: 34
Joined: Thu Aug 20, 2009 6:27 pm
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Re: Arctangent confusing to me

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

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
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Re: Arctangent confusing to me

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