Find the value of $ an( heta)$ on the unit circle when $ heta = frac{pi}{4}$.
Answer 1
Ava Martin
First, we need to determine the coordinates of the point on the unit circle corresponding to $\theta = \frac{\pi}{4}$.
On the unit circle, the coordinates for the angle $\frac{\pi}{4}$ are $\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$.
The tangent of an angle $\theta$ is given by the ratio of the y-coordinate to the x-coordinate of the corresponding point on the unit circle:
$\tan\left(\frac{\pi}{4}\right) = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$
So, the value of $\tan(\theta)$ for $\theta = \frac{\pi}{4}$ is 1.
Answer 2
Amelia Mitchell
The angle $frac{pi}{4}$ is located in the first quadrant of the unit circle.
In this quadrant, the coordinates of the point are $left(frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.
The tangent function is the ratio of the y-coordinate to the x-coordinate:
$ anleft(frac{pi}{4}
ight) = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1$
Therefore, $ an( heta)$ for $ heta = frac{pi}{4}$ is 1.
Answer 3
Emily Hall
For $ heta = frac{pi}{4}$, the coordinates on the unit circle are $left(frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.
Thus, $ anleft(frac{pi}{4}
ight) = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1$.
Hence, $ an( heta) = 1$ for $ heta = frac{pi}{4}$.
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