Find the Coordinate on the Unit Circle

Given the angle $\theta = \frac{\pi}{4}$, find the coordinate on the unit circle.

The angle $\theta = \frac{\pi}{4}$ is equivalent to 45 degrees. At this angle, both the x and y coordinates are equal. Since we are on the unit circle, the coordinates can be determined by the values of $\cos\theta$ and $\sin\theta$.

$x = \cos\left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2}$

$y = \sin\left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2}$

Thus, the coordinate on the unit circle is:

$\left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)$

Given the angle $ heta = frac{pi}{4}$, find the coordinate on the unit circle.

To find the coordinates, we use the trigonometric functions $cos heta$ and $sin heta$. For $ heta = frac{pi}{4}$:

$cosleft( frac{pi}{4}
ight) = frac{sqrt{2}}{2}$

$sinleft( frac{pi}{4}
ight) = frac{sqrt{2}}{2}$

Therefore, the coordinates are:

$left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$

Given $ heta = frac{pi}{4}$, the unit circle coordinate is:

$left( cosleft( frac{pi}{4}
ight), sinleft( frac{pi}{4}
ight)
ight) = left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$

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