Find the sine and cosine values for $frac{pi}{4}$ using the unit circle.
Answer 1
John Anderson
To find the sine and cosine values for $\frac{\pi}{4}$ using the unit circle, we use the coordinates of the point corresponding to that angle on the circle.
The angle $\frac{\pi}{4}$ is equivalent to 45 degrees. On the unit circle, the coordinates of the point at this angle are $\left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)$.
Therefore:
$\sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}$
$\cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}$
Answer 2
Isabella Walker
Using the unit circle, we determine the sine and cosine values for $frac{pi}{4}$.
The unit circle tells us that the coordinates at angle $frac{pi}{4}$ are $left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.
From this, we can write:
$sinleft(frac{pi}{4}
ight) = frac{sqrt{2}}{2}$
$cosleft(frac{pi}{4}
ight) = frac{sqrt{2}}{2}$
Answer 3
Michael Moore
For $frac{pi}{4}$ on the unit circle, the coordinates are $left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.
Thus:
$sinleft(frac{pi}{4}
ight) = frac{sqrt{2}}{2}$
$cosleft(frac{pi}{4}
ight) = frac{sqrt{2}}{2}$
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