$Find the value of an( heta) where heta is angle on the unit circle$
Answer 1
Amelia Mitchell
Consider the angle $\theta = \frac{\pi}{4}$ on the unit circle.
We know that $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$.
Since $\sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ and $\cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$, we get:
$\tan(\frac{\pi}{4}) = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$
Therefore, $\tan(\frac{\pi}{4}) = 1$.
Answer 2
Charlotte Davis
Consider the angle $ heta = frac{pi}{6}$ on the unit circle.
We know that $ an( heta) = frac{sin( heta)}{cos( heta)}$.
Since $sin(frac{pi}{6}) = frac{1}{2}$ and $cos(frac{pi}{6}) = frac{sqrt{3}}{2}$, we get:
$ an(frac{pi}{6}) = frac{frac{1}{2}}{frac{sqrt{3}}{2}} = frac{1}{sqrt{3}} = frac{sqrt{3}}{3}$
Therefore, $ an(frac{pi}{6}) = frac{sqrt{3}}{3}$.
Answer 3
Ava Martin
Consider the angle $ heta = frac{pi}{3}$ on the unit circle.
We know that $ an( heta) = frac{sin( heta)}{cos( heta)}$.
Since $sin(frac{pi}{3}) = frac{sqrt{3}}{2}$ and $cos(frac{pi}{3}) = frac{1}{2}$, we get:
$ an(frac{pi}{3}) = frac{frac{sqrt{3}}{2}}{frac{1}{2}} = sqrt{3}$
Therefore, $ an(frac{pi}{3}) = sqrt{3}$.
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