Describe the unit circle and determine the coordinates of a point with a given angle

The unit circle is a circle with a radius of 1, centered at the origin of the coordinate plane, i.e., at (0, 0). The equation of the unit circle is:

$ x^2 + y^2 = 1 $

Given an angle $\theta$ measured in radians from the positive x-axis, the coordinates $(x, y)$ of the corresponding point on the unit circle can be determined using trigonometric functions:

$ x = \cos(\theta) $

$ y = \sin(\theta) $

For example, if $\theta = \frac{\pi}{4}$:

$ x = \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} $

$ y = \sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} $

So, the coordinates of the point are:

$ \left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) $

The unit circle has a radius of 1 and is centered at the origin (0, 0). The equation is:

$ x^2 + y^2 = 1 $

For an angle $ heta$, the coordinates of the point are given by:

$ x = cos( heta) $

$ y = sin( heta) $

For instance, if $ heta = frac{pi}{3}$:

$ x = cosleft(frac{pi}{3}
ight) = frac{1}{2} $

$ y = sinleft(frac{pi}{3}
ight) = frac{sqrt{3}}{2} $

Thus, the coordinates are:

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

The unit circle has a radius of 1 and is centered at the origin (0, 0), described by:

$ x^2 + y^2 = 1 $

For an angle $ heta$, the coordinates $(x,y)$ are:

$ x = cos( heta) $

$ y = sin( heta) $

If $ heta = frac{pi}{6}$, then:

$ x = cosleft(frac{pi}{6}
ight) = frac{sqrt{3}}{2} $

$ y = sinleft(frac{pi}{6}
ight) = frac{1}{2} $

Coordinates are:

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

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