$ ext{Find the value of tangent for given angles on the unit circle}$
Answer 1
John Anderson
Given the angle $\theta = \frac{\pi}{4}$, we need to find the value of $\tan(\theta)$.
On the unit circle, the coordinates for $\theta = \frac{\pi}{4}$ are $(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$.
The tangent of an angle is given by the ratio of the y-coordinate to the x-coordinate:
$\tan(\frac{\pi}{4}) = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$
Thus, the value of $\tan(\frac{\pi}{4})$ is $1$.
Answer 2
Maria Rodriguez
Given the angle $ heta = frac{pi}{6}$, we need to find the value of $ an( heta)$.
On the unit circle, the coordinates for $ heta = frac{pi}{6}$ are $(frac{sqrt{3}}{2}, frac{1}{2})$.
The tangent of an angle is given by the ratio of the y-coordinate to the x-coordinate:
$ an(frac{pi}{6}) = frac{frac{1}{2}}{frac{sqrt{3}}{2}} = frac{1}{sqrt{3}} = frac{sqrt{3}}{3}$
Thus, the value of $ an(frac{pi}{6})$ is $frac{sqrt{3}}{3}$.
Answer 3
Lily Perez
Given the angle $ heta = frac{pi}{3}$, we need to find the value of $ an( heta)$.
On the unit circle, the coordinates for $ heta = frac{pi}{3}$ are $(frac{1}{2}, frac{sqrt{3}}{2})$.
The tangent of an angle is given by the ratio of the y-coordinate to the x-coordinate:
$ 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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