Calculus 2: Parametrized curves

Using parameterization, find the coordinates of a point on the unit circle given an angle $\theta$.

Graph the parametric equations $x=2t$ and $y=t^2$ by picking some $t$ values and finding the corresponding $x$ and $y$ values. Plot the points and connect them to see the resulting parabola.

Parametrize the unit circle in the XY-plane in XYZ space using trigonometry, with $R(T) = (\cos(T), \sin(T), 0)$ for T in $[0, 2\pi]$.

Parametrize the straight line segment from point P to point Q using $R(T) = (1-T) \cdot OP + T \cdot OQ$ for T in $[0,1]$.