Find the value of $ cos(frac{pi}{4}) $ and $ sin(frac{pi}{4}) $ using the unit circle
Answer 1
Amelia Mitchell
To find the values of $ \cos(\frac{\pi}{4}) $ and $ \sin(\frac{\pi}{4}) $ using the unit circle, we need to identify the coordinate point on the unit circle that corresponds to the angle $ \frac{\pi}{4} $.
The angle $ \frac{\pi}{4} $ is located in the first quadrant where both sine and cosine values are positive. This angle corresponds to the point $ (\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}) $ on the unit circle.
Therefore:
$ \cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2} $
$ \sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2} $
Answer 2
Charlotte Davis
Using the unit circle, the angle $ frac{pi}{4} $ is in the first quadrant. At $ frac{pi}{4} $, the coordinates on the unit circle are $ (frac{sqrt{2}}{2}, frac{sqrt{2}}{2}) $.
Hence:
$ cos(frac{pi}{4}) = frac{sqrt{2}}{2} $
$ sin(frac{pi}{4}) = frac{sqrt{2}}{2} $
Answer 3
James Taylor
From the unit circle:
$ cos(frac{pi}{4}) = frac{sqrt{2}}{2} $
$ sin(frac{pi}{4}) = frac{sqrt{2}}{2} $
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