$Convert the angle 150^{circ} to radians and find its coordinates on the unit circle.$

To convert degrees to radians, we use the conversion factor \( \frac{\pi}{180} \).

$150^{\circ} \times \frac{\pi}{180} = \frac{150\pi}{180} = \frac{5\pi}{6}$

The coordinates on the unit circle for \( \theta = \frac{5\pi}{6} \) are given by \((\cos(\theta), \sin(\theta))\).

$\cos\left(\frac{5\pi}{6}\right) = -\frac{\sqrt{3}}{2}, \sin\left(\frac{5\pi}{6}\right) = \frac{1}{2}$

Thus, the coordinates are:

$( -\frac{\sqrt{3}}{2}, \frac{1}{2} )$

First, convert the angle from degrees to radians:

$150^{circ} = 150 imes frac{pi}{180} = frac{5pi}{6}$

Next, use the unit circle to find the coordinates. The coordinates for ( heta = frac{5pi}{6} ) are:

$cosleft(frac{5pi}{6}
ight) = -frac{sqrt{3}}{2}, sinleft(frac{5pi}{6}
ight) = frac{1}{2}$

So, the coordinates are:

$( -frac{sqrt{3}}{2}, frac{1}{2} )$

Find the radian measure:

$150^{circ} = frac{5pi}{6}$

Coordinates:

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

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