' - - File XII_Family8.txt
pi = 3.14159

'  Find the tangent lines at pi/6 position

R{t} = 3 + 8 * Sin[2*pi*t]
a0=.2                                                     ' Original constant. Set pi/6 to, a NUMERICAL value.
 
X{t} = R{t} * Cos[2*pi*t] / 2                  ' Divide by 2 to scale the graph.
Y{t} = R{t} * Sin[2*pi*t] / 2
P<t> = <X,Y,0>

D<t> = vDiff[P]

T<t> = vDiv[D,sMag[D] ]              ' dR/dt / |Dr/dt |  =  dR/ds  = T (tangent vector)
Rn<t> =vEval[P,a0]
Tn<t> = vEval[T,a0]
L<t> = vAdd[vMpy[Tn,#],Rn]       ' Tangent line; # is parameter position.
t0 = 0  :  tf = 2  :  n = 100
Plot[P, L, {t, t0, tf, n}]


