Determine the values of $ an( heta) $ on the unit circle where $ an( heta) = 1 $ or $ an( heta) = -1 $
Answer 1
Ella Lewis
First, note that $ \tan(\theta) = 1 $ when $ \theta = \frac{\pi}{4} $ or $ \theta = \frac{5\pi}{4} $ on the unit circle. Also, $ \tan(\theta) = -1 $ when $ \theta = \frac{3\pi}{4} $ or $ \theta = \frac{7\pi}{4} $. Therefore, the angles where $ \tan(\theta) = 1 $ or $ \tan(\theta) = -1 $ are:
$ \theta = \frac{\pi}{4}, \frac{5\pi}{4}, \frac{3\pi}{4}, \frac{7\pi}{4} $
Answer 2
Emily Hall
To find where $ an( heta) = 1 $ on the unit circle, $ heta $ must be $ frac{pi}{4} $ or $ frac{5pi}{4} $. For $ an( heta) = -1 $, $ heta $ must be $ frac{3pi}{4} $ or $ frac{7pi}{4} $. Therefore:
$ heta = frac{pi}{4}, frac{5pi}{4}, frac{3pi}{4}, frac{7pi}{4} $
Answer 3
Maria Rodriguez
On the unit circle, $ an( heta) = 1 $ if $ heta = frac{pi}{4} $ or $ heta = frac{5pi}{4} $. For $ an( heta) = -1 $, $ heta = frac{3pi}{4} $ or $ heta = frac{7pi}{4} $. Thus:
$ heta = frac{pi}{4}, frac{5pi}{4}, frac{3pi}{4}, frac{7pi}{4} $
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