Find the sine and cosine values for the angle $frac{5pi}{6}$ on the unit circle, and determine the corresponding point on the unit circle.
Answer 1
Samuel Scott
First, we need to determine the reference angle for $\frac{5\pi}{6}$. The reference angle is $\pi – \frac{5\pi}{6} = \frac{\pi}{6}$.
In the second quadrant, sine is positive and cosine is negative.
The sine value for $\frac{\pi}{6}$ is $\sin\left(\frac{\pi}{6}\right) = \frac{1}{2}$.
The cosine value for $\frac{\pi}{6}$ is $\cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}$.
Therefore, $\sin\left(\frac{5\pi}{6}\right) = \frac{1}{2}$ and $\cos\left(\frac{5\pi}{6}\right) = -\frac{\sqrt{3}}{2}$.
The corresponding point on the unit circle is $\left(-\frac{\sqrt{3}}{2}, \frac{1}{2}\right)$.
Answer 2
Michael Moore
To find the sine and cosine values for $frac{5pi}{6}$, we first find the reference angle $pi – frac{5pi}{6} = frac{pi}{6}$.
In the second quadrant, sine remains positive while cosine is negative.
Knowing $sinleft(frac{pi}{6}
ight) = frac{1}{2}$ and $cosleft(frac{pi}{6}
ight) = frac{sqrt{3}}{2}$, we get:
$sinleft(frac{5pi}{6}
ight) = frac{1}{2}$
$cosleft(frac{5pi}{6}
ight) = -frac{sqrt{3}}{2}$
Hence, the coordinates on the unit circle are $left(-frac{sqrt{3}}{2}, frac{1}{2}
ight)$.
Answer 3
Ava Martin
The reference angle for $frac{5pi}{6}$ is $frac{pi}{6}$.
In the second quadrant:
$sinleft(frac{5pi}{6}
ight) = frac{1}{2}$
$cosleft(frac{5pi}{6}
ight) = -frac{sqrt{3}}{2}$
The point is $left(-frac{sqrt{3}}{2}, frac{1}{2}
ight)$.
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