Assignment 4

22

ParametricPlot3D[{Sin[t], Cos[t], Sin[t]^2}, {t, 0, 
        2  π}]

s1 = 
        ParametricPlot3D[{u, v, u^2}, {u, -1.25, 1.25}, {v, -1.5, 
            1.5}];

s2  = 
        ParametricPlot3D[{Cos[t], Sin[t], v}, {t, 0, 2  π}, {v, -1.1, 
            1.1}];

Show[s1, s2];

24

ParametricPlot3D[{t^4 - t^2 + 1, t, t^2}, {t, -1.5, 
          1.5}];

26

ParametricPlot3D[{Sin[t], Sin[2  t], Sin[3  t]}, {t, 0, 
        2  π}]

27

ParametricPlot3D[{(1 + Cos[16  t]) Cos[t], (1 + Cos[16  t]) 
          Sin[t], 1 + Cos[16  t]}, {t, 0, 2  π}, 
      PlotPoints -> 150]

28

ParametricPlot3D[{(Sqrt[1  -  0.25  Cos[t]^2]) 
            Cos[t], (Sqrt[1  -  0.25  Cos[t]^2]) Sin[t], 
          0.5 Cos[10  t]}, {t, 0, 
          2  π}, 
PlotPoints -> 150];

34

Solve[16 - t^2 - 4  t^4 == 0] // N

ParametricPlot3D[{t, 
          t^2, (1/2) (Sqrt[16 - t^2 - 4  t^4])}, {t, -1.37, 1.37}, 
        ViewPoint -> {2.5, 4, 2}];

s1  =  
        ParametricPlot3D[{Cos[u], Sin[u] Cos[v]/2, Sin[u] Sin[v]/2}, {u, 0, 
            2  π}, {v, 0, 2  π}];

s2  =  
        ParametricPlot3D[{u, u^2, v}, {u, -1, 1}, {v, -1, 
            1}];

Show[s1, s2, ViewPoint -> {2.5, 4, 2}];