Find the coordinates on the unit circle corresponding to an angle of $ heta $

To find the coordinates on the unit circle for an angle $ \theta $, we use the trigonometric functions sine and cosine. The coordinates are given by:

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$ (x, y) = (\cos(\theta), \sin(\theta)) $

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

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

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

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Thus, the coordinates are:

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

To find the coordinates on the unit circle for an angle $ heta $, use the following relationships:

$ (x, y) = (cos( heta), sin( heta)) $

For instance, for $ heta = frac{pi}{3} $:

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

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

Therefore, the coordinates are:

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

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

$ (x, y) = (cos( heta), sin( heta)) $

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

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

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

Thus, the coordinates are:

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

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