Find the exact values of $ sinleft(frac{3pi}{4}
ight) $ and $ cosleft(frac{3pi}{4}
ight) $ using the unit circle
Answer 1
Michael Moore
To find the exact values of $ \sin\left(\frac{3\pi}{4}\right) $ and $ \cos\left(\frac{3\pi}{4}\right) $, we use the unit circle:
$ \sin\left(\frac{3\pi}{4}\right) $ is located in the second quadrant, where the sine value is positive and the corresponding reference angle is $ \frac{\pi}{4} $. Therefore,
$ \sin\left(\frac{3\pi}{4}\right) = \sin\left(\pi – \frac{\pi}{4}\right) = \sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} $
Similarly, $ \cos\left(\frac{3\pi}{4}\right) $ is also in the second quadrant, where the cosine value is negative:
$ \cos\left(\frac{3\pi}{4}\right) = \cos\left(\pi – \frac{\pi}{4}\right) = -\cos\left(\frac{\pi}{4}\right) = -\frac{\sqrt{2}}{2} $
Answer 2
Matthew Carter
To find $ sinleft(frac{3pi}{4}
ight) $ and $ cosleft(frac{3pi}{4}
ight) $:
Using reference angles on the unit circle:
$ sinleft(frac{3pi}{4}
ight) = frac{sqrt{2}}{2} $
$ cosleft(frac{3pi}{4}
ight) = -frac{sqrt{2}}{2} $
Answer 3
Emma Johnson
Using the unit circle,
$ sinleft(frac{3pi}{4}
ight) = frac{sqrt{2}}{2} $
$ cosleft(frac{3pi}{4}
ight) = -frac{sqrt{2}}{2} $
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