Find the coordinates of the point on the unit circle corresponding to $210^{circ}$.

The unit circle is a circle with radius 1 centered at the origin (0,0) in the coordinate plane. Points on the unit circle can be represented as (cos θ, sin θ), where θ is the angle in degrees.

To find the coordinates of the point on the unit circle corresponding to $210^{\circ}$:

1. Convert the angle to radians: $210^{\circ} = \frac{210 \pi}{180} = \frac{7 \pi}{6}$.

2. Use the unit circle values:

$\cos \left(\frac{7 \pi}{6} \right) = -\frac{\sqrt{3}}{2}$

$\sin \left(\frac{7 \pi}{6} \right) = -\frac{1}{2}$

Thus, the coordinates are $\left( -\frac{\sqrt{3}}{2}, -\frac{1}{2} \right)$.

We follow these steps to determine the coordinates on the unit circle for $210^{circ}$.

Step 1: Convert the angle to radians, as unit circle angles are typically in radians:

$210^{circ} = frac{210 pi}{180} = frac{7 pi}{6}$

Step 2: Find the cosine and sine of $frac{7 pi}{6}$:

$cos left(frac{7 pi}{6}
ight) = -frac{sqrt{3}}{2}$

$sin left(frac{7 pi}{6}
ight) = -frac{1}{2}$

The coordinates at this angle are $left( -frac{sqrt{3}}{2}, -frac{1}{2}
ight)$.

Given $210^{circ}$:

Convert to radians:

$210^{circ} = frac{7 pi}{6}$

Then, calculate:

$cos left(frac{7 pi}{6}
ight) = -frac{sqrt{3}}{2}$

$sin left(frac{7 pi}{6}
ight) = -frac{1}{2}$

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

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