What is the tan value for the angle $ heta = frac{pi}{4} $ on the unit circle?
Answer 1
Emily Hall
To find the tan value for the angle $ \theta = \frac{\pi}{4} $ on the unit circle, we use the fact that $ \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} $.
The sine and cosine values for $ \theta = \frac{\pi}{4} $ are both $ \frac{\sqrt{2}}{2} $.
Therefore,
$ \tan\left( \frac{\pi}{4} \right) = \frac{ \sin\left( \frac{\pi}{4} \right) }{ \cos\left( \frac{\pi}{4} \right) } = \frac{ \frac{\sqrt{2}}{2} }{ \frac{\sqrt{2}}{2} } = 1 $
Answer 2
Isabella Walker
To determine $ anleft( frac{pi}{4}
ight) $, we substitute the known sine and cosine values at this angle. Both $ sinleft( frac{pi}{4}
ight) $ and $ cosleft( frac{pi}{4}
ight) $ are $ frac{sqrt{2}}{2} $.
Thus,
$ anleft( frac{pi}{4}
ight) = frac{ sinleft( frac{pi}{4}
ight) }{ cosleft( frac{pi}{4}
ight) } = frac{ frac{sqrt{2}}{2} }{ frac{sqrt{2}}{2} } = 1 $
Answer 3
Henry Green
For the angle $ heta = frac{pi}{4} $,
$ anleft( frac{pi}{4}
ight) = frac{ sinleft( frac{pi}{4}
ight) }{ cosleft( frac{pi}{4}
ight) } = frac{ frac{sqrt{2}}{2} }{ frac{sqrt{2}}{2} } = 1 $
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