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?