Given a point on the unit circle at angle $ heta $, determine the coordinates of the point and the angle $ heta $ in radians.

The unit circle is defined as the set of points (x,y) such that $x^2 + y^2 = 1$. For a point on the unit circle at an angle $ \theta $, the coordinates of the point are $(\cos(\theta),\sin(\theta))$.

For example, if $ \theta = \frac{\pi}{4} $, then:

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

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

Thus, the coordinates of the point are $\left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)$. So, the answer is $\theta = \frac{\pi}{4}$ rad.

The coordinates of a point on the unit circle at angle $ heta $ can be found using the trigonometric functions cos and sin. Specifically, the coordinates are $(cos( heta), sin( heta))$.

For $ heta = frac{pi}{3} $:

$ x = cosleft(frac{pi}{3}
ight) = frac{1}{2} $

$ y = sinleft(frac{pi}{3}
ight) = frac{sqrt{3}}{2} $

So, the coordinates of the point are $left( frac{1}{2}, frac{sqrt{3}}{2}
ight)$ and $ heta = frac{pi}{3}$ rad.

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

For example, if $ heta = frac{pi}{6} $, then:

$ x = cosleft(frac{pi}{6}
ight) = frac{sqrt{3}}{2} $

$ y = sinleft(frac{pi}{6}
ight) = frac{1}{2} $

The point is $left( frac{sqrt{3}}{2}, frac{1}{2}
ight)$ and $ heta = frac{pi}{6}$ rad.

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