$ ext{What is the sine of } 30^{circ} ext{ on the unit circle?}$

To find the sine of 30 degrees on the unit circle, we need to identify the coordinates of the point on the unit circle corresponding to this angle.

In the unit circle, each point is represented as $(\cos \theta, \sin \theta)$. For an angle of $30^{\circ}$, the coordinates are given by:

$\left( \cos 30^{\circ}, \sin 30^{\circ} \right) = \left( \frac{\sqrt{3}}{2}, \frac{1}{2} \right)$

Therefore, the sine of $30^{\circ}$ is:

$\sin 30^{\circ} = \frac{1}{2}$

The unit circle provides a simple way to find trigonometric values. For $30^{circ}$, we use the fact that the sine of an angle is equal to the y-coordinate of the corresponding point on the unit circle.

For $30^{circ}$, the coordinates are:

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

This means:

$sin 30^{circ} = frac{1}{2}$

At $30^{circ}$ on the unit circle, the coordinates are:

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

So:

$sin 30^{circ} = frac{1}{2}$

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