Consider the parametric equations x$($t$)=2$cost$$and$$y$($t$)=2$sint$$on the interval $0$t$<2$$.$

What shape do these equations parameterize?

Write the corresponding cartesian equation.$$

Calculate the slope of the tangent line on this curve at t$=3$$4.$

At what value$($s$)$ of t are there horizontal tangent lines on this curve? What about vertical tangent lines?

Calculate the length of the curve between t$=$$3$ and t$=11$$6.$