Find the sine, cosine, and tangent values for the angle $frac{pi}{4}$ on the unit circle.
Answer 1
Michael Moore
To find the sine, cosine, and tangent values for the angle $\frac{\pi}{4}$ on the unit circle, we first recognize that $\frac{\pi}{4}$ is a standard angle.
The coordinates for this angle on the unit circle are $\left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)$.
Therefore, the sine value is the y-coordinate:
$ \sin \left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2} $
The cosine value is the x-coordinate:
$ \cos \left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2} $
The tangent value is the ratio of the sine to the cosine:
$ \tan \left( \frac{\pi}{4} \right) = \frac{\sin \left( \frac{\pi}{4} \right)}{\cos \left( \frac{\pi}{4} \right)} = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1 $
Answer 2
Lily Perez
Let’s determine the sine, cosine, and tangent for the angle $frac{pi}{4}$ on the unit circle.
At this angle, the unit circle coordinates are $left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.
Thus, we have:
$ sin left( frac{pi}{4}
ight) = frac{sqrt{2}}{2} $
$ cos left( frac{pi}{4}
ight) = frac{sqrt{2}}{2} $
$ an left( frac{pi}{4}
ight) = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1 $
Answer 3
John Anderson
For the angle $frac{pi}{4}$, the unit circle coordinates are $left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.
Therefore:
$ sin left( frac{pi}{4}
ight) = frac{sqrt{2}}{2} $
$ cos left( frac{pi}{4}
ight) = frac{sqrt{2}}{2} $
$ an left( frac{pi}{4}
ight) = 1 $
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