input fonctions; u = 10cm; verbatimtex %&latex \documentclass{minimal} \usepackage[garamond]{mathdesign} \begin{document} etex vardef Y(expr t) = u * (sin(t) ** 2) enddef; vardef Z(expr t) = u * ((cos(t + .5 * (sin(t)**2)))**2) enddef; vardef R(expr t) = u / 2 * (1 + .8 * sin(2*t + (sin(t)**2))) enddef;beginfig(1); drawarrow (0,0) -- (0,1.2u) withpen pencircle scaled 1.5pt; drawarrow (0,0) -- (1.2u,0) withpen pencircle scaled 1.5pt; draw (.5u,.01u) -- (.5u,-.01u); draw (u,.01u) -- (u,-.01u); draw (-.01u,.5u) -- (.01u,.5u); draw (-.01u,u) -- (.01u,u) ; label.llft(btex $O$ etex scaled 2,(0,0)); label.lft(btex $0.5$ etex scaled 2, (-.01u,.5u)); label.lft(btex $1$ etex scaled 2, (-.01u,u)); label.bot(btex $0.5$ etex scaled 2, (0.5u,-.01u)); label.bot(btex $1$ etex scaled 2, (u,-.01u)); label.bot(btex $y$ etex scaled 2, (1.2u,-.01u)); label.lft(btex $z$ etex scaled 2, (-.01u,1.2u)); dt = Pi/100; draw (Y(0),Z(0)) ... for i:=1 upto 100: (Y(i*dt),Z(i*dt)) ... endfor cycle withpen pencircle scaled 2.5pt withcolor (.9,.7,.6); drawarrow (0,u) -- (.2u,.8u) withcolor (.1,.3,.4); label(btex \(y =\sin^2 t\quad z= \cos^2(t +\frac12\sin^2t)\) etex scaled 2.5,(.6u,-.2u)); endfig;
beginfig(2); drawarrow (0,0) -- (0,u) withpen pencircle scaled 1.5pt; drawarrow (0,0) -- (1.7u,0) withpen pencircle scaled 1.5pt; draw ((Pi/4)*u,.01u) -- ((Pi/4)*u,-.01u); draw ((Pi/2)*u,.01u) -- ((Pi/2)*u,-.01u); draw (-.01u,.5u) -- (.01u,.5u); label.llft(btex $O$ etex scaled 2,(0,0)); label.lft(btex $1$ etex scaled 2, (-.01u,.5u)); label.bot(btex $\pi/2$ etex scaled 2, ((Pi/4)*u,-.01u)); label.bot(btex $\pi$ etex scaled 2, ((Pi/2)*u,-.01u)); label.bot(btex $t$ etex scaled 2, (1.7u,-.01u)); label.lft(btex $R$ etex scaled 2, (-.01u,u)); draw (0,R(0)) for i:=1 upto 100: ... (i*dt*u/2,R(i*dt)) endfor withpen pencircle scaled 2.5pt withcolor (.7,.8,.9); label(btex \(R = 1 + \frac45\sin(2t+\sin^2t)\) etex scaled 2.5,(.85u,-.2u)); endfig; end