It can be the basis of the trig functions because the hypotenuse, which is the radius, is 1.
For related reasons, it can represent unit vectors in any direction.
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If you draw a unit circle, the sine function can be expressed as the y-coordinate of a point on the circle; the cosine function as the x-coordinate.
If the radius is two. it won't be a unit circle, a unit circle is defined as a circle with radius one.
The unit circle is a circle with its center at the origin and a radius of ' 1 '.
A unit circle is a circle with radius equal to one.
The period of a trigonometric function, since it depends on the angle of a ray centered in a unit circle, is 2 pi radians or 360 degrees.