I. Substituting the parametric equations $$x(t)=\cos(t)$$ and $$y(t)=\sin(t)$$ into the implicit equation $$x^2+y^2=1$$ yields the identity $$\cos^2(t)+\sin^2(t)=1$$.

II. The parameterization $$x(t)=\cos(t)$$, $$y(t)=\sin(t)$$ covers only the upper half of the circle.

III. The parameterization represents a circle of radius 1.

Which of these statements are true regarding the parameterization of the circle given by $$x^2+y^2=1$$?