Find the coordinates of the point on the unit circle for an angle of $ frac{3pi}{4} $ radians

To find the coordinates of the point on the unit circle for an angle of $ \frac{3\pi}{4} $ radians, we need to use the unit circle definition:

For an angle $ \theta $, the coordinates are given by:

$ (\cos(\theta), \sin(\theta)) $

Here, $ \theta = \frac{3\pi}{4} $

So,

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

and

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

The coordinates are:

$ \left( -\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) $

To find the coordinates of the point on the unit circle for an angle of $ frac{3pi}{4} $ radians, we use:

$ (cos( heta), sin( heta)) $

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

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

and

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

Hence, the coordinates are:

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

For the angle $ frac{3pi}{4} $:

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

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

Thus, the coordinates are:

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

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