Find the sine and cosine values for the angle $frac{5pi}{6}$
Answer 1
Chloe Evans
To find the sine and cosine values for the angle $\frac{5\pi}{6}$, we first understand that this angle is located in the second quadrant of the unit circle.
The reference angle for $\frac{5\pi}{6}$ is $\pi – \frac{5\pi}{6} = \frac{\pi}{6}$.
We know the sine and cosine values for $\frac{\pi}{6}$ are $\sin\left(\frac{\pi}{6}\right) = \frac{1}{2}$ and $\cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}$.
Since $\frac{5\pi}{6}$ is in the second quadrant, the sine value remains positive, and the cosine value becomes negative.
Therefore, $\sin\left(\frac{5\pi}{6}\right) = \frac{1}{2}$ and $\cos\left(\frac{5\pi}{6}\right) = -\frac{\sqrt{3}}{2}$.
Answer 2
Michael Moore
The angle $frac{5pi}{6}$ is in the second quadrant. To find the sine and cosine, we use the reference angle: $frac{pi}{6}$.
The known values for $frac{pi}{6}$ are $sinleft(frac{pi}{6}
ight) = frac{1}{2}$ and $cosleft(frac{pi}{6}
ight) = frac{sqrt{3}}{2}$.
In the second quadrant, sine is positive and cosine is negative.
Thus, the values for $frac{5pi}{6}$ are: $sinleft(frac{5pi}{6}
ight) = frac{1}{2}$ and $cosleft(frac{5pi}{6}
ight) = -frac{sqrt{3}}{2}$.
Answer 3
Ava Martin
For the angle $frac{5pi}{6}$ in the second quadrant, with reference angle $frac{pi}{6}$:
$sinleft(frac{5pi}{6}
ight) = frac{1}{2}$, $cosleft(frac{5pi}{6}
ight) = -frac{sqrt{3}}{2}$.
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