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DrawingCurvesOnASphere::usage="The title indicates everything. References: Hollis, Selwyn. CalcLabs with Mathematica, Multivariable ​​ Calculus. 4a. Ed, Cengage Learning: pp. 179-181; Personal.";
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​​Animate[wireSphere=SphericalPlot3D[1,{ϕ,0,π},{θ,0,2π},Mesh{12,24},MeshStyle->Gray,PlotStyleNone];Show[wireSphere,ParametricPlot3D[{Cos[t]Sin[t],Sin[t]Sin[t],Cos[t]},{t,0,θ}],BoxedFalse,AxesNone],{θ,0.01,2π},AnimationRunning->False]
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Animate[wireSphere=SphericalPlot3D[1,{ϕ,0,π},{θ,0,2π},Mesh{12,24},MeshStyle->Gray,PlotStyleNone];Show[wireSphere,ParametricPlot3D[{Cos[t]Sin[2t],Sin[t]Sin[2t],Cos[2t]},{t,0,θ}],BoxedFalse,AxesNone],{θ,0.01,2π},AnimationRunning->False]
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Animate[wireSphere=SphericalPlot3D[1,{ϕ,0,π},{θ,0,2π},Mesh{12,24},MeshStyle->Gray,PlotStyleNone];​​Show[wireSphere,ParametricPlot3D[{Cos[6t]Sin[t],Sin[6t]Sin[t],Cos[t]},{t,0,θ}],BoxedFalse,AxesNone],{θ,0.01,π},AnimationRunning->False]
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AnimatewireSphere=SphericalPlot3D[1,{ϕ,0,π},{θ,0,2π},Mesh{12,24},MeshStyle->Gray,PlotStyleNone];ShowwireSphere,ParametricPlot3DCos[-5πt]
2
t
,Sin[-5πt]
2
t
,
1-
4
t
,{t,0,t1},BoxedFalse,AxesNone,{t1,0.01,1},AnimationRunning->False
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AnimatewireSphere=SphericalPlot3D[1,{ϕ,0,π},{θ,0,2π},Mesh{12,24},MeshStyle->Gray,PlotStyleNone];ShowwireSphere,ParametricPlot3DCos[-5πt]
1-
1
2
(t+1)
,Sin[-5πt]
1-
1
2
(t+1)
,
1
(t+1)
,{t,0,t1},BoxedFalse,AxesNone,{t1,0.01,1},AnimationRunning->False
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AnimatewireSphere=SphericalPlot3D[1,{ϕ,0,π},{θ,0,2π},Mesh{12,24},MeshStyle->Gray,PlotStyleNone];ShowwireSphere,ParametricPlot3DCos[4πt]
1-
2
2
π
ArcTan[t]
,Sin[-5πt]
1-
2
2
π
ArcTan[t]
,
2
π
ArcTan[t],{t,0,t1},BoxedFalse,AxesNone,{t1,0.01,1},AnimationRunning->False