Final answer:
The statement that the unit circle on the coordinate plane has a radius of 1 unit is true.
Step-by-step explanation:
The question presented is whether it is true that the unit circle on the coordinate plane has a radius of 1 unit. This is indeed true. In mathematics, the unit circle is a circle with a radius of exactly one unit, usually centered at the origin (0,0) of the coordinate plane. The property of the unit circle being one unit in radius is fundamental in understanding concepts related to trigonometry and the Pythagorean theorem.
For example, if an angle is placed in the unit circle such that its vertex is at the origin and one side lies along the x-axis, the coordinates of the intersection of the other side of the angle with the unit circle can be used to define the sine and cosine of the angle. Moreover, the existence of the unit vector in polar coordinates is based on the radial distance being one.
The Pythagorean theorem can be used to relate the x and y coordinates of a point on the unit circle to its radius. Since the circle has a radius of one, the equation x^2 + y^2 = 1 holds for any point on the unit circle.