Finding the Coordinates of a Point on the Unit Circle

Given an angle of $\theta = \frac{\pi}{3}$ radians, find the coordinates of the corresponding point on the unit circle.

First, recall the unit circle definition: for any angle $\theta$, the coordinates of the point on the unit circle are given by $(\cos \theta, \sin \theta)$. For $\theta = \frac{\pi}{3}$:

$\cos \left( \frac{\pi}{3} \right) = \frac{1}{2}$

$\sin \left( \frac{\pi}{3} \right) = \frac{\sqrt{3}}{2}$

Thus, the coordinates are:

$(\frac{1}{2}, \frac{\sqrt{3}}{2})$

Determine the coordinates of the point on the unit circle for the angle $ heta = frac{pi}{3}$ radians.

We use the unit circle property: the coordinates for angle $ heta$ are $(cos heta, sin heta)$. For $ heta = frac{pi}{3}$, we get:

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

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

Therefore, the coordinates are:

$(frac{1}{2}, frac{sqrt{3}}{2})$

Find the coordinates of the point on the unit circle for $ heta = frac{pi}{3}$ radians.

The unit circle coordinates are given by $(cos heta, sin heta)$.

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

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

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

Therefore:

$(frac{1}{2}, frac{sqrt{3}}{2})$

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