Determine the coordinates of the point on the unit circle corresponding to a given angle $ heta$

To determine the coordinates of the point on the unit circle corresponding to the angle $\theta$, we use the following formulas for the unit circle:

$ x = \cos(\theta) $

$ y = \sin(\theta) $

For instance, 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} $

So, the coordinates are:

$ \left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right) $

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

$ x = cos( heta) $

$ y = 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} $

The coordinates are:

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

To locate coordinates on the unit circle for angle $ heta$:

$ x = cos( heta) $

$ y = sin( heta) $

For $ heta = frac{pi}{6}$:

$ left(cosleft(frac{pi}{6}
ight), sinleft(frac{pi}{6}
ight)
ight) = left(frac{sqrt{3}}{2}, frac{1}{2}
ight) $

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