Math 2060 - Section 13.2

2063 days ago by jimlb

Section 13.2

In this worksheet we just give one example of the tangent vectors moving along a curve.  


Example:  Consider the curve ${\bf r}(t) = \langle t, \cos (t) \rangle$.   The first animation gives the vectors ${\bf r}(t)$ as $t$ moves as red arrows.  The tangent vectors are given by the green arrows.

step=0.75 P=Graphics() v=[] for n in srange(0,9): P+=plot(f(t), (t,0, 2*pi)); P+=arrow((0,0),(0.1+n*step,f(0.1+n*step)),color='red') P+=arrow((0.1+n*step,f(0.1+n*step)), (1.1+n*step, f(0.1+n*step)-sin(0.1+n*step)), color='green') v.append(P) a = animate(v,xmin=0) a.show(delay = 150) 
       

It may also be easier to see the tangent vectors ${\bf r'}(t)$ without the vectors ${\bf r}(t)$ as well. That is given in the following animation. 

step=0.75 P=Graphics() v=[] for n in srange(0,9): P+=plot(f(t), (t,0, 2*pi)); P+=arrow((0.1+n*step,f(0.1+n*step)), (1.1+n*step, f(0.1+n*step)-sin(0.1+n*step)), color='green') v.append(P) a = animate(v,xmin=0) a.show(delay = 150)