Find the coordinates on the unit circle for an angle of $frac{pi}{4}$

To find the coordinates on the unit circle for an angle of $\frac{\pi}{4}$, we need to use the unit circle definition.

The unit circle has a radius of 1, and the coordinates for any angle $\theta$ can be found using $\cos(\theta)$ and $\sin(\theta)$.

For $\theta = \frac{\pi}{4}$, we have:

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

and

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

Thus, the coordinates are:

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

To determine the coordinates on the unit circle for an angle of $frac{pi}{4}$, we rely on trigonometric functions.

Using the unit circle, where the radius is 1, the coordinates for an angle $ heta$ are $(cos( heta), sin( heta))$.

For $ heta = frac{pi}{4}$, the trigonometric values are:

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

and

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

Therefore, the coordinates are:

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

In order to find the coordinates on the unit circle for an angle of $frac{pi}{4}$, use the unit circle properties:

For $ heta = frac{pi}{4}$:

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

and

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

Thus, the coordinates are:

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

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