%% auteur : gh

150 setxunit
-0.5 3 setxrange
-0.5 2 setyrange

traceaxes
axesarrow
1.7 setlinewidth

/O {0 0} def
16 setfontsize
setTimesItalic
   (O) O dltext

/rho {pi 2 div sub Cos 1 add} def
/rho' {Cos} def

/X {dup rho exch Cos mul} def
/Y {dup rho exch Sin mul} def

/X' {settvar t rho' t Cos mul t rho t Sin mul sub} def
/Y' {settvar t rho' t Sin mul t rho t Cos mul add} def

-1 1.2 settrange
{X} {Y} courbeparam

/t 0.24 def
/Mt {t X t Y} def
/vt {t X' t Y'} def
/ut {t Cos t Sin} def
/ut' {t Sin neg t Cos} def 
/fx {Mt ut t rho' mulv addv} def
/fy {Mt ut' t rho mulv addv} def

rouge
Mt point
Mt vt vect
<tex>
$$ \vec{f}'(\theta) $$
</tex>
Mt Mt vt addv milieu [1.5 1.5] drtexlabel
0.2 setlinewidth
Mt Mt vt addv droite
fx Mt vt addv (-) line
fy Mt vt addv (-) line
<tex>
$$ \rho'(\theta) $$
</tex>
fx [1 1] drtexlabel
<tex>
$$ \rho(\theta) $$
</tex>
fy [1 1] dltexlabel
bleu
O Mt  droite
Mt Mt ut' addv droite
1.7 setlinewidth
Mt ut vect
<tex>
$$ \vec{u}(\theta) $$
</tex>
Mt Mt ut addv milieu [1.5 1.5] drtexlabel
Mt ut' vect
<tex>
$$ \vec{u}'(\theta) $$
</tex>
Mt Mt ut' addv milieu [1.5 1.5] dltexlabel

1 setlinewidth
/arrowangle -5 store
1 0 O Mt 0.4 (->) tripointarc
<tex>
$$ \theta$$
</tex>
O t 2 div Cos t 2 div Sin 0.4 mulv addv  [1.5 1.5] crtexlabel