Find the coordinates of the point on the unit circle at angle $pi/3$ radians.

To find the coordinates of the point on the unit circle at angle $\pi/3$ radians, we use the unit circle definitions. The unit circle is defined by the equation $x^2 + y^2 = 1$, where the coordinates $(x, y)$ correspond to $(\cos(\theta), \sin(\theta))$ for an angle $\theta$.

For $\theta = \pi/3$:

$x = \cos(\pi/3) = \frac{1}{2}$

$y = \sin(\pi/3) = \frac{\sqrt{3}}{2}$

Thus, the coordinates are $\left( \frac{1}{2}, \frac{\sqrt{3}}{2} \right)$.

Using the unit circle, the coordinates for any angle $ heta$ can be determined as $(cos( heta), sin( heta))$.

Given $ heta = pi/3$, we find:

$cos(pi/3) = frac{1}{2}$

$sin(pi/3) = frac{sqrt{3}}{2}$

So the point is $left( frac{1}{2}, frac{sqrt{3}}{2}
ight)$.

For an angle $pi/3$ radians on the unit circle:

$cos(pi/3) = frac{1}{2}$ and $sin(pi/3) = frac{sqrt{3}}{2}$

The coordinates are $left( frac{1}{2}, frac{sqrt{3}}{2}
ight)$.

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