Graphics3D[Tube[Table[{Cos[t], Sin[t], t/π}, {t, -2π, 2π, π/24}], .05], Axes -> True, AxesLabel ->{x,y,z}]

The helix is the range (or image) of the vector valued function
(Subscript[r, c])(t) = (cos(t), sin(t), t/π)

Question:
Find the tangent line to the helix at the point (((Sqrt[3])/2),(1/2),(1/6)).  That is, find the function (Subscript[r, l])(t) whose range (or image) is the tangent line.

r0 = {};
v = {};
Print["Tangent line at r0 = ", r0, ", with velocity vector v = ", v, " is drawn."];Graphics3D[{Tube[Table[{Cos[t], Sin[t], t/π}, {t, -2π, 2π, π/24}], .05],Tube[Table[r0+ v t, {t, -2π, 2π, π}], .05]}, PlotRange ->{{-2,2}, {-2,2}, {-2, 2}}, Axes -> True, AxesLabel ->{x,y,z}]

The helix and the tangent line at the point (cos(a), sin(a), a/π).  This occurs at t = a.  This next cell gives the tangent line at any time t = a.

a = π/3;
r0 = {Cos[a], Sin[a], a/π};
v = {-Sin[a], Cos[a], 1/π};
Print["Tangent line at r0 = ", r0, ", with velocity vector v = ", v, " is drawn."];Graphics3D[{Tube[Table[{Cos[t], Sin[t], t/π}, {t, -2π, 2π, π/24}], .05],Tube[Table[r0+ v t, {t, -2π, 2π, π}], .05]}, PlotRange ->{{-2,2}, {-2,2}, {-2, 2}}, Axes -> True, AxesLabel ->{x,y,z}]

Just for fun, here is a trefoil knot.  The wikipedia article on the trefoil knot has the parameterization I use here.

Graphics3D[Tube[Table[{Sin[t] + 2 Sin[2t], Cos[t] - 2 Cos[2t], -Sin[3t]}, {t, 0, 2 π, π/100}], .1 ] ]

You can also use the built-in functions and data in Mathematica to plot the trefoil knot.

KnotData["trefoil"]