Identify the coordinates of points on the unit circle for given angles $ heta $
Answer 1
Isabella Walker
For the angle $ \theta = \frac{\pi}{6} $, the point on the unit circle is given by $ (\cos(\frac{\pi}{6}), \sin(\frac{\pi}{6})) $.
Calculate these values:
$ \cos(\frac{\pi}{6}) = \frac{\sqrt{3}}{2} $
$ \sin(\frac{\pi}{6}) = \frac{1}{2} $
Therefore, the coordinates are:
$ (\frac{\sqrt{3}}{2}, \frac{1}{2}) $
Answer 2
Joseph Robinson
For the angle $ heta = frac{pi}{4} $, the point on the unit circle is given by $ (cos(frac{pi}{4}), sin(frac{pi}{4})) $.
Calculate these values:
$ cos(frac{pi}{4}) = frac{sqrt{2}}{2} $
$ sin(frac{pi}{4}) = frac{sqrt{2}}{2} $
Therefore, the coordinates are:
$ (frac{sqrt{2}}{2}, frac{sqrt{2}}{2}) $
Answer 3
James Taylor
For the angle $ heta = frac{pi}{3} $, the point on the unit circle is:
$ (cos(frac{pi}{3}), sin(frac{pi}{3})) = (frac{1}{2}, frac{sqrt{3}}{2}) $
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