Find the sine of $frac{pi}{6}$ on the unit circle.

To find the sine of $\frac{\pi}{6}$ on the unit circle, we need to know the coordinates of the point on the unit circle corresponding to this angle. The unit circle has a radius of 1, and an angle of $\frac{\pi}{6}$ corresponds to 30 degrees in the first quadrant.

The coordinates of this point on the unit circle are $\left( \frac{\sqrt{3}}{2}, \frac{1}{2} \right)$. The y-coordinate of this point gives us the sine value.

Therefore,

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

First, we recognize that the angle $frac{pi}{6}$ is equal to 30 degrees. On the unit circle, this angle is found in the first quadrant.

The coordinates on the unit circle for an angle of $frac{pi}{6}$ are: $left( cosleft(frac{pi}{6}
ight), sinleft(frac{pi}{6}
ight)
ight)$

Using known values, we have:

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

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

So,

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

At $frac{pi}{6}$, the corresponding y-coordinate on the unit circle is the sine value.

Thus,

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

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