Find the coordinates of the point on the unit circle corresponding to an angle of $ heta = frac{pi}{4}$
Answer 1
William King
For an angle \(\theta = \frac{\pi}{4}\) on the unit circle, we use the trigonometric functions sine and cosine to find the coordinates. The coordinates are given by \((\cos \theta, \sin \theta)\).
$ \cos \frac{\pi}{4} = \frac{\sqrt{2}}{2} $
$ \sin \frac{\pi}{4} = \frac{\sqrt{2}}{2} $
Therefore, the coordinates are $ \left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) $
Answer 2
Amelia Mitchell
On the unit circle, coordinates for any angle ( heta) are determined by ( cos heta ) and ( sin heta ). Given ( heta = frac{pi}{4} ), we find:
$ cos frac{pi}{4} = frac{sqrt{2}}{2} $
$ sin frac{pi}{4} = frac{sqrt{2}}{2} $
Hence, the location on the unit circle is $ left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) $
Answer 3
Abigail Nelson
The unit circle coordinates for ( heta = frac{pi}{4} ) are found as follows:
$ cos frac{pi}{4} = frac{sqrt{2}}{2} $
$ sin frac{pi}{4} = frac{sqrt{2}}{2} $
Coordinates: $ left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) $
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