With a parametric plot and a set of t values we can associat

With a parametric plot and a set of t values, we can associate a \'direction\'. For example, the curve (cos t, sin t) is the unit circle traced counterclockwise. How can we amend a set of given parametric equations and t values to get the same curve, only traced backwards?

Solution

Let r(t)=<cost, sint>

This circle is traced counterclockwise. In order to get the same circle with backward trace, we simply need to multiply the second term by -1, so, the curve with backward trace is R(t)=<cost, -sint>