What is the definition of a unit circle?

The unit circle is specifically defined as a circle that has a radius of 1 and is centered at the origin of a coordinate plane. This definition is fundamental in trigonometry and serves as a basis for defining the sine and cosine functions, as the coordinates of any point on the unit circle correspond to these trigonometric values.

In the context of the unit circle, the radius of 1 means that every point on the circle is exactly one unit away from the center, which is the origin at (0, 0). This relationship enables easy calculation of angles and their corresponding sine and cosine values, which are simply the x and y coordinates of points on the circle.

The other options do not meet the specific criteria that define the unit circle. While a circle with a diameter of 1 can be related to the unit circle (as it would have a radius of 0.5), it does not fit the required characteristics. Similarly, a circle centered at the origin or a circle with a radius of 2 doesn’t satisfy both conditions of having a radius of 1 and being centered at the origin. Thus, the most accurate and precise description of the unit circle is indeed as a circle with a radius of 1, centered at the