Find the sine and cosine of the angle where the terminal side intersects the unit circle at the point $ left( -frac{1}{2}, frac{sqrt{3}}{2}
ight) $.

To find the sine and cosine of the angle whose terminal side intersects the unit circle at the point $ \left( -\frac{1}{2}, \frac{\sqrt{3}}{2} \right) $, we start by identifying the coordinates of the point on the unit circle.

The x-coordinate, $ x = -\frac{1}{2} $, represents the cosine of the angle.

The y-coordinate, $ y = \frac{\sqrt{3}}{2} $, represents the sine of the angle.

Therefore, the cosine of the angle is:

$ \cos(\theta) = -\frac{1}{2} $

And the sine of the angle is:

$ \sin(\theta) = \frac{\sqrt{3}}{2} $

Given the point $ left( -frac{1}{2}, frac{sqrt{3}}{2}
ight) $ on the unit circle, we need to determine the sine and cosine of the corresponding angle.

The cosine value corresponds to the x-coordinate, and the sine value corresponds to the y-coordinate of the point.

Therefore:

$ cos( heta) = -frac{1}{2} $

$ sin( heta) = frac{sqrt{3}}{2} $

The angle where the terminal side intersects the unit circle at this point has a cosine of $ -frac{1}{2} $ and a sine of $ frac{sqrt{3}}{2} $.

For the point $ left( -frac{1}{2}, frac{sqrt{3}}{2}
ight) $ on the unit circle:

$ cos( heta) = -frac{1}{2} $

$ sin( heta) = frac{sqrt{3}}{2} $

These values correspond to the cosine and sine of the angle.

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