[justify]We define a circle as the set of points on a plane that are equidistant from a point [math]\left(x_{0,} \ y_0\right)[/math], which is the center of the circle. The distance from each point of the circle to the center is called the radius. The equation of a circle centered at [math]\left(x_{0,} \ y_0\right)[/math] with radius [math]r[/math] is [/justify][center][math] \large \left(x-x_0\right)^2 - \left( y - y_0\right)^2 = r^2. [/math] [/center][br]The [b]unit circle[/b] is the circle centered at the origin with radius of 1 unit, so the equation of the [b]unit circle[/b] is[br][br][center][math] \huge x^2+y^2=1.[/math][/center][br]The unit circle is shown below. The point on the unit circle can be moved, showing the approximate coordinates.  Note the right triangle formed by mapping out the coordinates. Note that the equation [math]x^2+y^2=1[/math]  is simply an application of the [url=https://tube.geogebra.org/material/simple/id/222063]Pythagorean theorem[/url].