Plot[Cos[t] Sin[Sin[t]], {t, 0, 2 Pi}]

Integrate[Cos[t] Sin[Sin[t]], {t, 0, 2 Pi}]

Integrate[Cos[t] Sin[Sin[t]], t]

{(y/((x^2) + (y^2))), -(x/((x^2) + (y^2)))}

Simplify[D[-(x/((x^2) + (y^2))), x]]

Simplify[D[(y/((x^2) + (y^2))), y]]

Simplify[
      Simplify[({(y/((x^2) + (y^2))), -(x/((x^2) + 
                        (y^2)))} /. {x -> Cos[t], 
                y -> Sin[t]})] . D[{Cos[t], Sin[t]}, t]]

{(y/((x^2) + (y^2))), -(x/((x^2) + (y^2)))}

Integrate[(y/((x^2) + (y^2))), x]

Simplify[D[ArcTan[(x/y)], y]]

Simplify[{D[ArcTan[(x/y)], x], D[ArcTan[(x/y)], y]}]

<< Graphics`ImplicitPlot`

pl1=ImplicitPlot[x^3 + y^3 == 3 x y , {x, -2, 2}, {y, -2, 2}]

pl2 = 
      ParametricPlot[{((3 t)/(1 + t^3)), ((3 t^2)/(1 + t^3))}, {t, 0, 
          20}, PlotStyle -> {Thickness[0.01], Yellow}]

Show[pl2, pl1]

{0, x} /. {x ->  ((3 t)/(1 + t^3)), 
        y ->  ((3 t^2)/(1 + t^3))}