Determine the values of $ sin( heta) $, $ cos( heta) $, and $ an( heta) $ for $ heta $ in the second quadrant of the unit circle

In the second quadrant, the angle $ \theta $ ranges from $ \frac{\pi}{2} $ to $ \pi $. Here, $ \sin(\theta) $ is positive, $ \cos(\theta) $ is negative, and $ \tan(\theta) $ is negative.

Using the unit circle, for $ \theta = \frac{2\pi}{3} $:

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

$ \cos(\frac{2\pi}{3}) = -\frac{1}{2} $

$ \tan(\frac{2\pi}{3}) = -\sqrt{3} $

In the second quadrant, the angle $ heta $ ranges from $ frac{pi}{2} $ to $ pi $. Here, $ sin( heta) $ is positive, $ cos( heta) $ is negative, and $ an( heta) $ is negative.

Using the unit circle, for $ heta = frac{3pi}{4} $:

$ sin(frac{3pi}{4}) = frac{sqrt{2}}{2} $

$ cos(frac{3pi}{4}) = -frac{sqrt{2}}{2} $

$ an(frac{3pi}{4}) = -1 $

In the second quadrant, the angle $ heta $ ranges from $ frac{pi}{2} $ to $ pi $. Here, $ sin( heta) $ is positive, $ cos( heta) $ is negative, and $ an( heta) $ is negative.

Using the unit circle, for $ heta = frac{5pi}{6} $:

$ sin(frac{5pi}{6}) = frac{1}{2} $

$ cos(frac{5pi}{6}) = -frac{sqrt{3}}{2} $

$ an(frac{5pi}{6}) = -frac{1}{sqrt{3}} $

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