Question

: More Information in Parametric Equations. In this section we stated that parametric equations contain more information than just the shape of a curve. Write a short paragraph explaining this statement. Use the following example and your answers to parts (a) and (b) below in your explanation. The position of a particle is given by the parametric equations

where represents time. We know that the shape of the path of the particle is a circle.

How long does it take the particle to go once around the circle? Find parametric equations if the particle moves twice as fast around the circle.