Determine the quadrant of point P on the unit circle where $P$ has coordinates $(cos( heta), sin( heta))$, given that $ heta = 210$ degrees.

First, convert the given angle to radians:

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

Determine the coordinates of point P:

$P = (\cos(210^\circ), \sin(210^\circ))$

Since $210^\circ$ is in the third quadrant, $\cos(210^\circ)$ is negative and $\sin(210^\circ)$ is also negative. Therefore, the point P is in the third quadrant.

The answer is: The point P is in the third quadrant.

Convert the given angle to radian measure:

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

Identify the quadrant of the angle:

An angle of $210^circ$ is $30^circ$ past $180^circ$, which places it in the third quadrant. In the third quadrant, both sine and cosine are negative.

The coordinates of point P are:

$P = (cos(210^circ), sin(210^circ))$

Since $cos(210^circ) < 0$ and $sin(210^circ) < 0$, the point P is indeed in the third quadrant.

The answer is: Third quadrant.

Convert $210^circ$ to radians:

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

Since $210^circ$ lies in the third quadrant ($180^circ$ to $270^circ$), both cosine and sine are negative.

The coordinates of point P are $(cos(210^circ), sin(210^circ))$, which confirms that P is in the third quadrant.

The answer is: Third quadrant.

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