Find the cosine and sine values for $frac{5pi}{6}$ radians in the unit circle.
Answer 1
Benjamin Clark
To find the cosine and sine values for $\frac{5\pi}{6}$ radians in the unit circle, we start by recognizing that $\frac{5\pi}{6}$ is in the second quadrant.
In the second quadrant, the angle is $\pi – \theta$. Here, $\theta = \frac{\pi}{6}$.
Therefore, we have:
$\cos(\frac{5\pi}{6}) = \cos(\pi – \frac{\pi}{6}) = -\cos(\frac{\pi}{6}) = -\frac{\sqrt{3}}{2}$
$\sin(\frac{5\pi}{6}) = \sin(\pi – \frac{\pi}{6}) = \sin(\frac{\pi}{6}) = \frac{1}{2}$
So, the cosine value is $-\frac{\sqrt{3}}{2}$ and the sine value is $\frac{1}{2}$.
Answer 2
Mia Harris
We need to find the cosine and sine values for $frac{5pi}{6}$ radians.
First, identify its reference angle, $frac{pi}{6}$. Since $frac{5pi}{6}$ is in the second quadrant, cosine is negative and sine is positive.
Thus,
$cos(frac{5pi}{6}) = -cos(frac{pi}{6}) = -frac{sqrt{3}}{2}$
$sin(frac{5pi}{6}) = sin(frac{pi}{6}) = frac{1}{2}$
The cosine value is $-frac{sqrt{3}}{2}$ and the sine value is $frac{1}{2}$.
Answer 3
Chloe Evans
For $frac{5pi}{6}$ radians, recognize it’s in the second quadrant.
$cos(frac{5pi}{6}) = -frac{sqrt{3}}{2}$
$sin(frac{5pi}{6}) = frac{1}{2}$
The cosine value is $-frac{sqrt{3}}{2}$ and the sine value is $frac{1}{2}$.
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