Final answer:
The question involves converting standard equations into parametric form. Parts (a) and (b) describe a circle, while parts (c) and (d) describe different parabolic trajectories, all using 't' as the parameter.
Step-by-step explanation:
The question involves converting given equations into their parametric forms. When equations are expressed in terms of a parameter (commonly t), each variable is defined as a function of that parameter.
a) The given equations x = sin(t) and y = cos(t) are already in parametric form, representing a circle with a radius of 1, centered at the origin in the Cartesian plane.
b) Similarly, x = cos(t) and y = sin(t) also represent a circle with a radius of 1, centered at the origin, parameterized differently from part (a).
c) For x = 2t and y = t2, these equations describe a parabolic trajectory, where t is the parameter. As t varies, x changes linearly, and y changes quadratically.
d) The final set, x = t2 and y = 2t also describes a parabolic path but oriented differently relative to the coordinate axes than in part (c).