Parametric Equations for the Unit Circle

Consider the parameterization given by the equations $x(t)=\cos(t)$ and $y(t)=\sin(t)$, which corresponds to the rectangular equation $x^2+y^2=1$.

I. Substituting the parametric equations into the rectangular equation results in the identity $\cos^2(t)+\sin^2(t)=1$.

II. The curve traced by the parameterization is only the upper half of the circle.

III. The parameterization represents a circle with a radius of 1.

Which of the above statements are true?