Determine the coordinates of the point on the unit circle for an angle of $frac{5pi}{6}$ radians. Also, find the corresponding angle in degrees.

To determine the coordinates of the point on the unit circle corresponding to an angle of $\frac{5\pi}{6}$ radians, we follow these steps:

1. Convert the angle into degrees:

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

2. Find the coordinates using trigonometric functions on the unit circle:

$x = \cos(150^\circ) = \cos(180^\circ – 30^\circ) = -\cos(30^\circ) = -\frac{\sqrt{3}}{2}$

$y = \sin(150^\circ) = \sin(180^\circ – 30^\circ) = \sin(30^\circ) = \frac{1}{2}$

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

The corresponding angle in degrees is $150^\circ$.

To find the coordinates on the unit circle for $frac{5pi}{6}$ radians and the angle in degrees:

1. Convert radians to degrees:

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

2. Use the unit circle to find $x$ and $y$ coordinates:

$x = cos(150^circ) = -frac{sqrt{3}}{2}$

$y = sin(150^circ) = frac{1}{2}$

Therefore, the coordinates are $left( -frac{sqrt{3}}{2}, frac{1}{2}
ight)$

The angle in degrees is $150^circ$.

For $frac{5pi}{6}$ radians:

1. Convert to degrees:

$150^circ$

2. Coordinates:

$x = -frac{sqrt{3}}{2}, y = frac{1}{2}$

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

Angle: $150^circ$

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