Find the exact values of $ sin( heta) $, $ cos( heta) $, and $ an( heta) $ for $ heta = frac{3pi}{4} $

Consider the angle $ \theta = \frac{3\pi}{4} $, which is in the second quadrant.

Using the unit circle, we know:

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

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

$ \tan(\frac{3\pi}{4}) = \frac{\sin(\frac{3\pi}{4})}{\cos(\frac{3\pi}{4})} = \frac{\frac{\sqrt{2}}{2}}{-\frac{\sqrt{2}}{2}} = -1 $

For $ heta = frac{3pi}{4} $:

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

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

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

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 $

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