Find the value of $ an( heta) $ using the unit circle when $ heta = frac{3pi}{4} $
Answer 1
John Anderson
We need to find the value of $ \tan(\theta) $ where $ \theta = \frac{3\pi}{4} $ using the unit circle. The coordinates of the point on the unit circle corresponding to $ \theta = \frac{3\pi}{4} $ are:
$ \left( -\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) $
Recall that $ \tan(\theta) = \frac{y}{x} $. Therefore:
$ \tan \left( \frac{3\pi}{4} \right) = \frac{\frac{\sqrt{2}}{2}}{-\frac{\sqrt{2}}{2}} = -1 $
Answer 2
Lucas Brown
To find the value of $ an left( frac{5pi}{6}
ight) $ using the unit circle, we first find the coordinates of the point corresponding to $ frac{5pi}{6} $:
$ left( -frac{sqrt{3}}{2}, frac{1}{2}
ight) $
Since $ an( heta) = frac{y}{x} $:
$ an left( frac{5pi}{6}
ight) = frac{frac{1}{2}}{-frac{sqrt{3}}{2}} = -frac{1}{sqrt{3}} = -frac{sqrt{3}}{3} $
Answer 3
Ava Martin
To find $ an left( frac{pi}{3}
ight) $ using the unit circle, the coordinates of the point are:
$ left( frac{1}{2}, frac{sqrt{3}}{2}
ight) $
Thus:
$ an left( frac{pi}{3}
ight) = frac{frac{sqrt{3}}{2}}{frac{1}{2}} = sqrt{3} $
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