Trig/ Pre Cal How do I determine what quadrant this is in? 2 owlbucks! \[ \tan^-1(\tan(\frac{5\pi}{6})) \] Thank you.

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Trig/ Pre Cal How do I determine what quadrant this is in? 2 owlbucks! \[ \tan^-1(\tan(\frac{5\pi}{6})) \] Thank you.

Mathematics
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It was suppose to be \[ \tan^1(\tan\frac{5\pi}{6}) \] I don't know how to make the -1 power so 1 = -1. It is an inverse
I'm not sure what you mean... You mean where it is on the unit circle?
Just a number does not have a "quadrant".

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Btw to make an exponent negative, just do tan^{-1} in latex :)
Yes. For instance, we have a domain of \( -\frac{\pi}{2}< x< \frac{\pi}{2} \) and range of \( -infinity< x< infinity \)
How do I find the quadrant that \( \frac{5\pi}{6} lies in?\)
Easy way is to just look at the unit circle http://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/2000px-Unit_circle_angles_color.svg.png
I know by looking at the unit circle but lets say we had a strange angle like \( \frac{4\pi}{5} \)
\[\large \frac{\pi}{5} = \frac{180}{5} = 36~degrees\]So \[\large \frac{4\pi}{5} = 4 \times \frac{\pi}{5} = 4 \times 36 = 144\] Since 144 is above 90 but below 180, it would be in quadrant 2 :) Also if the numerator is lower than the denominator, you know it will be in it either the first or second quadrants
Thank you!!
I sent your owlbucks :-)

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