Find the value of $ an( heta)$ where $ heta$ is a special angle on the unit circle.
Answer 1
Matthew Carter
To find the value of $\tan(\theta)$ where $\theta$ is a special angle on the unit circle, we use the definition $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$.
For $\theta = \frac{\pi}{4}$, the sine and cosine values are both $\frac{\sqrt{2}}{2}$.
Therefore, $\tan(\frac{\pi}{4}) = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$.
Answer 2
Samuel Scott
To determine $ an( heta)$ for a special angle, we use $ an( heta) = frac{sin( heta)}{cos( heta)}$.
For $ heta = frac{2pi}{3}$, we have $sin(frac{2pi}{3}) = frac{sqrt{3}}{2}$ and $cos(frac{2pi}{3}) = -frac{1}{2}$.
Thus, $ an(frac{2pi}{3}) = frac{frac{sqrt{3}}{2}}{-frac{1}{2}} = -sqrt{3}$.
Answer 3
Charlotte Davis
We know $ an( heta) = frac{sin( heta)}{cos( heta)}$.
For $ heta = frac{5pi}{6}$, $sin(frac{5pi}{6}) = frac{1}{2}$ and $cos(frac{5pi}{6}) = -frac{sqrt{3}}{2}$.
Therefore, $ an(frac{5pi}{6}) = frac{frac{1}{2}}{-frac{sqrt{3}}{2}} = -frac{1}{sqrt{3}} = -frac{sqrt{3}}{3}$.
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