Find the coordinates of the point where the angle $ frac{pi}{4} $ intersects the unit circle
Answer 1
Benjamin Clark
To find the coordinates of the point where the angle $ \frac{\pi}{4} $ intersects the unit circle, we use the unit circle definition. The unit circle has a radius of 1, and the coordinates of the points on the circle are given by the cosine and sine of the angle.
For the angle $ \frac{\pi}{4} $, we have:
$ \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} $
$ \sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} $
Therefore, the coordinates are:
$ \left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) $
Answer 2
Amelia Mitchell
To find the coordinates of the point where the angle $ frac{pi}{4} $ intersects the unit circle, we know that the coordinates are given by $ ( cos( heta), sin( heta) ) $.
For $ heta = frac{pi}{4} $, we have:
$ cosleft(frac{pi}{4}
ight) = frac{sqrt{2}}{2} $
$ sinleft(frac{pi}{4}
ight) = frac{sqrt{2}}{2} $
Thus, the coordinates are:
$ left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) $
Answer 3
Daniel Carter
For the angle $ frac{pi}{4} $, the coordinates on the unit circle are:
$ left( cosleft(frac{pi}{4}
ight), sinleft(frac{pi}{4}
ight)
ight) = left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) $
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