Determine the sine and cosine values of an angle $ heta$ in radians on the unit circle given that $ heta = frac{5pi}{4}$.
Answer 1
Christopher Garcia
Given $\theta = \frac{5\pi}{4}$, we determine the sine and cosine values by examining the unit circle.
The angle $\frac{5\pi}{4}$ is located in the third quadrant, where sine and cosine values are negative. Specifically:
$ \sin \left( \frac{5\pi}{4} \right) = -\frac{\sqrt{2}}{2} $
$ \cos \left( \frac{5\pi}{4} \right) = -\frac{\sqrt{2}}{2} $
Answer 2
Emily Hall
When given $ heta = frac{5pi}{4}$, the sine and cosine values can be found using the unit circle. In the third quadrant:
$ sin left( frac{5pi}{4}
ight) = -frac{sqrt{2}}{2} $
$ cos left( frac{5pi}{4}
ight) = -frac{sqrt{2}}{2} $
Answer 3
Maria Rodriguez
For $ heta = frac{5pi}{4}$, the sine and cosine values are:
$ sin left( frac{5pi}{4}
ight) = -frac{sqrt{2}}{2} $
$ cos left( frac{5pi}{4}
ight) = -frac{sqrt{2}}{2} $
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