More on Plots

Plot[Sin[x], {x, -Pi, Pi}]

Plot3D[Sin[x y], {x, -Pi, Pi}, {y, -Pi, Pi}]

2D (Planar) Curves

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

Do[Do[
        ParametricPlot[{Sin[m t], Cos[n t]}, {t, -Pi, +Pi}], {n, 1, 
          3}], {m, 1, 3}]

Do[ParametricPlot[{Sin[t/(n 0.1)], 
          Cos[t]}, {t, -Pi, +Pi}], {n, 1, 9}]

Do[ParametricPlot[{Sin[t], Cos[n t]}, {t, -Pi, +Pi}], {n, 1, 
        9}]

Do[Do[
        ParametricPlot[{Sin[m t], Cos[n t]}, {t, -Pi, +Pi}], {n, 1, 
          3}], {m, 1, 3}]

Do[ParametricPlot[{Cos[t] (2 Cos[t] + 1), 
          Sin[t] (2 Cos[n t] + 1)}, {t, 0, 2 Pi}], {n, 1, 
        3}]

ParametricPlot[{3  t/(1 + t^3), 3  t^2/(1 + t^3)}, {t, -20, 
        20}, AspectRatio -> 1]

3D (Spatial) Curves

ParametricPlot3D[{Cos[t], Sin[t], 2 Sin[t/2]}, {t, 0, 
        4 Pi}]

ParametricPlot3D[{Cos[t], Sin[t], 2 Sin[t/2], Hue[Sin[t/8]]}, {t, 0, 
        4 Pi}]

ParametricPlot3D[{Cos[t], Sin[t], 2 Sin[t/3], Hue[Sin[t/12]]}, {t, 0, 
        6  Pi}]

ParametricPlot3D[{Cos[t], Sin[t], 2 Sin[t/3] Cos[t], 
        Hue[Sin[t/12]]}, {t, 0, 6  Pi}]

ParametricPlot3D[{Cos[t], Sin[t], 2 Sin[t/3] Cos[t], 
        Hue[Sin[t/12]]}, {t, 0, 6  Pi}, 
      ViewPoint -> {-3,  -1,  -2}]

ParametricPlot3D[{Cos[t], Sin[t], 2 Sin[t/3] Cos[t], 
        Hue[Sin[t/12]]}, {t, 0, 6  Pi}, 
      ViewPoint -> {-0.080,  -3.383,  -0.026}]

ParametricPlot3D[{Cos[t], Sin[t], 2 Sin[t/3] Cos[t], 
        Hue[Sin[t/12]]}, {t, 0, 6  Pi}, 
      ViewPoint -> {-0.080,  -3.383,  -0.026}, 
      Background -> GrayLevel[0.1]]

3D (Spatial) Surfaces

ParametricPlot3D[{x, y, x^2 - y^2}, {x, -2, 2}, {y, -2, 
        2}]

ParametricPlot3D[{x, y, x^2 - y^2}, {x, -2, 2}, {y, -2, 2}, 
      Background -> Hue[0]]

ParametricPlot3D[{x, y, x^3 - 3  x y^2}, {x, -2, 2}, {y, -2, 
        2}, AspectRatio -> 1]

ParametricPlot3D[{x, y, x^3 - 3  x y^2}, {x, -2, 2}, {y, -2, 
        2}, AspectRatio -> 1, 
      ViewPoint -> {-0.080,  -3.383,  -0.026}]

ParametricPlot3D[{x, y, x^3 - 3  x y^2}, {x, -2, 2}, {y, -2, 
        2}, AspectRatio -> 1, ViewPoint -> {2,  1,  5}]

saddle = {x, y, x^3 - 3  x y^2}

ParametricPlot3D[saddle, {x, -2, 2}, {y, -2, 2}, 
      AspectRatio -> 1, ViewPoint -> {2,  1,  5}]

flap[x_, y_, a_] := {x, y, x^3 - a x y^2}

ParametricPlot3D[flap[x, y, 1], {x, -2, 2}, {y, -2, 2}, 
      AspectRatio -> 1, ViewPoint -> {2,  1,  5}]

Do[ParametricPlot3D[flap[x, y, a], {x, -2, 2}, {y, -2, 2}, 
        AspectRatio -> 1, ViewPoint -> {2,  1,  5}], {a, 1, 
        3,  .2}]

Do[ParametricPlot3D[flap[x, y, a], {x, -2, 2}, {y, -2, 2}, 
        PlotRange -> {-20, 20}, ViewPoint -> {2,  1,  5}], {a, 1, 
        3,  .2}]

ParametricPlot3D[{Cos[x], Sin[y], Sin[x] Sin[y]}, {x, -2, 
        2}, {y, -2, 2}, AspectRatio -> 1, 
      ViewPoint -> {2,  1,  5}]

ParametricPlot3D[{Cos[x], Sin[y], Sin[x] Sin[y]}, {x, -2, 
        2}, {y, -2, 2}, AspectRatio -> 1, 
      ViewPoint -> {3,  -2,  0}]

ParametricPlot3D[{Cos[x], Sin[y], Sin[x] Sin[y]}, {x, -2, 
        2}, {y, -2, 2}, AspectRatio -> 1, 
      ViewPoint -> {3,  -9,  0}]

ParametricPlot3D[{Cos[x], Sin[y], Sin[x] Sin[y]}, {x, -2, 
        2}, {y, -2, 2}, AspectRatio -> 1, 
      ViewPoint -> {-1,  -3,  0}]

ParametricPlot3D[{Cos[x], Sin[y], Sin[x] Sin[y]}, {x, -2, 
        2}, {y, -2, 2}, AspectRatio -> 1, 
      ViewPoint -> {-3,  -3,  0}]

Do[ParametricPlot3D[{Cos[x], Sin[y], Sin[x] Sin[y]}, {x, -2, 
          2}, {y, -2, 2}, AspectRatio -> 1, 
        ViewPoint -> {Sin[n Pi 0.1], Cos[n Pi 0.1],  0}], {n, 0, 
        9}]