Find the coordinates of $ cos(frac{pi}{3}) $ on the unit circle
Answer 1
Henry Green
To find the coordinates of $ \cos(\frac{\pi}{3}) $ on the unit circle, we need to identify the coordinates associated with this angle.
On the unit circle, the angle $ \frac{\pi}{3} $ corresponds to the 60° position.
At this position, the coordinates are:
$ ( \cos(\frac{\pi}{3}), \sin(\frac{\pi}{3}) ) = ( \frac{1}{2}, \frac{\sqrt{3}}{2} ) $
Answer 2
Thomas Walker
To determine the value of $ sin(frac{pi}{4}) $ on the unit circle, we identify the coordinates associated with this angle.
On the unit circle, the angle $ frac{pi}{4} $ corresponds to the 45° position.
At this position, the coordinates are:
$ ( cos(frac{pi}{4}), sin(frac{pi}{4}) ) = ( frac{sqrt{2}}{2}, frac{sqrt{2}}{2} ) $
Thus, the value of $ sin(frac{pi}{4}) $ is:
$ sin(frac{pi}{4}) = frac{sqrt{2}}{2} $
Answer 3
Sophia Williams
To evaluate $ an(frac{pi}{6}) $ on the unit circle, we use the ratio of $ sin $ and $ cos $ functions.
On the unit circle, the angle $ frac{pi}{6} $ corresponds to the 30° position.
At this position, the coordinates are:
$ ( cos(frac{pi}{6}), sin(frac{pi}{6}) ) = ( frac{sqrt{3}}{2}, frac{1}{2} ) $
Thus, the value of $ an(frac{pi}{6}) $ is:
$ an(frac{pi}{6}) = frac{sin(frac{pi}{6})}{cos(frac{pi}{6})} = frac{frac{1}{2}}{frac{sqrt{3}}{2}} = frac{1}{sqrt{3}} = frac{sqrt{3}}{3} $
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