Given a point on the unit circle at an angle $ heta = frac{pi}{4}$, find the coordinates of the point.

We know that the coordinates of a point on the unit circle are given by $(\cos(\theta), \sin(\theta))$.

Given $\theta = \frac{\pi}{4}$:

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

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

So, the coordinates of the point are $\left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)$.

For a point on the unit circle, its coordinates are $(cos( heta), sin( heta))$.

Given $ heta = frac{pi}{4}$, we calculate:

$cosleft(frac{pi}{4}
ight) = frac{1}{sqrt{2}} = frac{sqrt{2}}{2}$

$sinleft(frac{pi}{4}
ight) = frac{1}{sqrt{2}} = frac{sqrt{2}}{2}$

Therefore, the coordinates are $left(frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.

The coordinates of a point on the unit circle at $ heta = frac{pi}{4}$ are:

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

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