Find the coordinates of the point on the unit circle at angle $ heta = frac{pi}{4} $

The coordinates of the point on the unit circle at angle $ \theta = \frac{\pi}{4} $ can be found using the sine and cosine functions:

The x-coordinate is:

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

The y-coordinate is:

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

Therefore, the coordinates are:

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

At angle $ heta = frac{pi}{4} $, the coordinates on the unit circle are:

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

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

Thus, the coordinates are:

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

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

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

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