Find the coordinates on the unit circle for an angle of $frac{5pi}{6}$

To find the coordinates of the point on the unit circle corresponding to an angle of $\frac{5\pi}{6}$, we can use the sine and cosine functions.

The angle $\frac{5\pi}{6}$ is in the second quadrant.

The reference angle is $\pi – \frac{5\pi}{6} = \frac{\pi}{6}$.

We know that for $\frac{\pi}{6}$:

$\cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}$

$\sin\left(\frac{\pi}{6}\right) = \frac{1}{2}$

Since $\frac{5\pi}{6}$ is in the second quadrant, the x-coordinate (cosine) will be negative and the y-coordinate (sine) will be positive.

Therefore, the coordinates are:

$\left(-\frac{\sqrt{3}}{2}, \frac{1}{2}\right)$

To determine the coordinates on the unit circle for an angle of $frac{5pi}{6}$, use the sine and cosine values.

$frac{5pi}{6}$ lies in the second quadrant.

The reference angle is $pi – frac{5pi}{6} = frac{pi}{6}$.

For $frac{pi}{6}$:

$cosleft(frac{pi}{6}
ight) = frac{sqrt{3}}{2}$

$sinleft(frac{pi}{6}
ight) = frac{1}{2}$

In the second quadrant, cosine is negative, and sine is positive.

Hence, the coordinates are:

$left(-frac{sqrt{3}}{2}, frac{1}{2}
ight)$

Find the coordinates for $frac{5pi}{6}$:

Reference angle: $frac{pi}{6}$.

$cosleft(frac{pi}{6}
ight) = frac{sqrt{3}}{2}$, $sinleft(frac{pi}{6}
ight) = frac{1}{2}$

Coordinates: $left(-frac{sqrt{3}}{2}, frac{1}{2}
ight)$

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