Find the sine and cosine values for the angle $frac{5pi}{6}$ using the unit circle.
Answer 1
Maria Rodriguez
First, locate the angle $\frac{5\pi}{6}$ on the unit circle.
The angle $\frac{5\pi}{6}$ is in the second quadrant.
In the second quadrant, sine is positive and cosine is negative.
The reference angle for $\frac{5\pi}{6}$ is $\pi – \frac{5\pi}{6} = \frac{\pi}{6}$.
From the unit circle, $\sin\left(\frac{\pi}{6}\right) = \frac{1}{2}$ and $\cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}$.
Thus, $\sin\left(\frac{5\pi}{6}\right) = \frac{1}{2}$ and $\cos\left(\frac{5\pi}{6}\right) = -\frac{\sqrt{3}}{2}$.
Answer 2
Lily Perez
Identify that $frac{5pi}{6}$ lies in the second quadrant.
In the second quadrant, sine values are positive, and cosine values are negative.
The reference angle is calculated as $pi – frac{5pi}{6} = frac{pi}{6}$.
From the unit circle, $sinleft(frac{pi}{6}
ight) = frac{1}{2}$ and $cosleft(frac{pi}{6}
ight) = frac{sqrt{3}}{2}$.
Therefore, $sinleft(frac{5pi}{6}
ight) = frac{1}{2}$ and $cosleft(frac{5pi}{6}
ight) = -frac{sqrt{3}}{2}$.
Answer 3
Thomas Walker
The angle $frac{5pi}{6}$ is in the second quadrant.
Reference angle $ = frac{pi}{6}$.
Thus, $sinleft(frac{5pi}{6}
ight) = frac{1}{2}$ and $cosleft(frac{5pi}{6}
ight)= -frac{sqrt{3}}{2}$.
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