Find $ sin( heta) $ and $ cos( heta) $ for $ heta $ on the unit circle

To find $ \sin(\theta) $ and $ \cos(\theta) $ when $ \theta $ is on the unit circle:

Recall the unit circle definition: the unit circle is a circle with a radius of 1 centered at the origin. Therefore, if $ (x, y) $ is a point on the unit circle corresponding to the angle $ \theta $, then:

$ \cos(\theta) = x $

$ \sin(\theta) = y $

For example, at $ \theta = \frac{\pi}{4} $, we have:

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

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

To find $ sin( heta) $ and $ cos( heta) $ for angles on the unit circle:

The unit circle has a radius of 1 and is centered at the origin. If $ (x, y) $ is a point on the unit circle, then $ cos( heta) $ is the x-coordinate and $ sin( heta) $ is the y-coordinate of that point. For example, for $ heta = frac{pi}{3} $:

$ cos left( frac{pi}{3}
ight) = frac{1}{2} $

$ sin left( frac{pi}{3}
ight) = frac{sqrt{3}}{2} $

To determine $ sin( heta) $ and $ cos( heta) $ on the unit circle, note:

If $ (x, y) $ is a point on the unit circle, then:

$ cos( heta) = x $

$ sin( heta) = y $

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