Find the sine and cosine of the angle $30^{circ}$ using the unit circle.

First, we need to convert $30^{\circ}$ to radians:

$30^{\circ} = 30 \times \frac{\pi}{180} = \frac{\pi}{6}$

On the unit circle, the coordinates of the angle $\frac{\pi}{6}$ are:

$\left( \cos\left(\frac{\pi}{6}\right), \sin\left(\frac{\pi}{6}\right) \right)$

Using known values, we have:

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

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

Therefore, the sine of $30^{\circ}$ is $\frac{1}{2}$ and the cosine of $30^{\circ}$ is $\frac{\sqrt{3}}{2}$.

To find the sine and cosine of $30^{circ}$, we first convert the angle to radians:

$30^{circ} = 30 imes frac{pi}{180} = frac{pi}{6}$

We know that the coordinates for an angle of $frac{pi}{6}$ on the unit circle are given by $(cos( heta), sin( heta))$ where $ heta = frac{pi}{6}$.

From trigonometric identities, we have:

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

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

Therefore, cosine of $30^{circ}$ is $frac{sqrt{3}}{2}$ and sine of $30^{circ}$ is $frac{1}{2}$.

Convert $30^{circ}$ to radians:

$30^{circ} = frac{pi}{6}$

The coordinates of $frac{pi}{6}$ on the unit circle are:

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

So, $cos(30^{circ}) = frac{sqrt{3}}{2}$ and $sin(30^{circ}) = frac{1}{2}$.

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