Find the coordinates of points on the unit circle corresponding to specific angles $ heta = frac{pi}{6}, heta = frac{pi}{4}, heta = frac{pi}{3} $

To find the coordinates of points on the unit circle corresponding to $ \theta = \frac{\pi}{6}, \theta = \frac{\pi}{4}, \theta = \frac{\pi}{3} $, we use the unit circle properties:

For $ \theta = \frac{\pi}{6} $:

$ (\cos(\frac{\pi}{6}), \sin(\frac{\pi}{6})) = \left( \frac{\sqrt{3}}{2}, \frac{1}{2} \right) $

For $ \theta = \frac{\pi}{4} $:

$ (\cos(\frac{\pi}{4}), \sin(\frac{\pi}{4})) = \left( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \right) $

For $ \theta = \frac{\pi}{3} $:

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

To find the coordinates of points on the unit circle corresponding to $ heta = frac{pi}{6}, heta = frac{pi}{4}, heta = frac{pi}{3} $:

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

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

For $ heta = frac{pi}{4} $:

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

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

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

To find the coordinates for $ heta = frac{pi}{6}, heta = frac{pi}{4}, heta = frac{pi}{3} $:

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

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