Find the coordinates of a point on the unit circle given the angle $ heta $

To find the coordinates of a point on the unit circle given an angle $ \theta $, we use the formulas for sine and cosine:

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$ x = \cos(\theta) $

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$ y = \sin(\theta) $

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

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

To find the coordinates of a point on the unit circle given an angle $ heta $, we use the formulas for sine and cosine:

$ x = cos( heta) $

$ y = sin( heta) $

For example, if $ heta = frac{pi}{3} $:

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

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

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

To find the coordinates of a point on the unit circle given an angle $ heta $, we use:

$ x = cos( heta) $

$ y = sin( heta) $

For $ heta = 0 $:

$ x = cos(0) = 1 $

$ y = sin(0) = 0 $

So the coordinates are $ (1, 0) $.

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