Find the coordinates of the point on the unit circle where the angle is $frac{3pi}{4}$ radians.
Answer 1
Emma Johnson
To find the coordinates of the point on the unit circle where the angle is $\frac{3\pi}{4}$ radians, we use the unit circle definition:
The coordinates are given by:
$ (\cos\theta, \sin\theta) $
For $ \theta = \frac{3\pi}{4} $:
$ \cos\left(\frac{3\pi}{4}\right) = -\frac{\sqrt{2}}{2} $
$ \sin\left(\frac{3\pi}{4}\right) = \frac{\sqrt{2}}{2} $
Therefore, the coordinates are:
$ \left( -\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) $
Answer 2
Christopher Garcia
To find the coordinates of the point on the unit circle where the angle is $frac{3pi}{4}$ radians, we use the unit circle definition:
The coordinates are $ (cos heta, sin heta) $.
For $ heta = 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) $
Answer 3
Mia Harris
For the angle $frac{3pi}{4}$ radians on the unit circle:
$ cosleft(frac{3pi}{4}
ight) = -frac{sqrt{2}}{2} $
$ sinleft(frac{3pi}{4}
ight) = frac{sqrt{2}}{2} $
Coordinates: $ left( -frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) $
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