Determine the coordinates of a point on the unit circle with a given angle, $ heta $

To determine the coordinates of a point on the unit circle given the angle $ \theta $, use the unit circle formulas:

$ x = \cos(\theta) $

$ y = \sin(\theta) $

For example, if $ \theta = 60^\circ $:

$ x = \cos(60^\circ) = \frac{1}{2} $

$ y = \sin(60^\circ) = \frac{\sqrt{3}}{2} $

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

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

$ x = cos( heta) $

$ y = sin( heta) $

For $ heta = 45^circ $:

$ x = cos(45^circ) = frac{sqrt{2}}{2} $

$ y = sin(45^circ) = frac{sqrt{2}}{2} $

The coordinates are $ left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) $.

To find the coordinates for $ heta = 30^circ $, use:

$ x = cos(30^circ) = frac{sqrt{3}}{2} $

$ y = sin(30^circ) = frac{1}{2} $

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

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