Calculate the coordinates of a point on the unit circle, given $ heta$ in radians.

To calculate the coordinates of a point on the unit circle given an angle $\theta$ in radians, use the formulas:

$ x = \cos(\theta) $

and

$ y = \sin(\theta) $

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

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

and

$ 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) $

Given $ heta$ in radians, the coordinates of a point on the unit circle can be found using:

$ x = cos( heta) $

and

$ y = sin( heta) $

As an example, if $ heta = frac{2pi}{3}$:

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

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

Thus, the coordinates are:

$ left( -frac{1}{2}, frac{sqrt{3}}{2}
ight) $

To find coordinates on the unit circle for a given angle $ heta$:

$ x = cos( heta) $

$ y = sin( heta) $

If $ heta = pi$, then:

$ x = cos(pi) = -1 $

$ y = sin(pi) = 0 $

Coordinates are:

$ (-1, 0) $

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