Fichier figure048.mp (figure 3) — Modifié le 10 Avril 2008 à 22 h 06

Source

%@AUTEUR:Guillaume Connan
prologues:=2;

verbatimtex
%&latex
\documentclass{article}
\usepackage{amsmath}
\begin{document}
etex

input courbes;
input geo;

color vert_e, turquoise, orange, vert_fonce, rose, vert_mer, bleu_ciel, or, rouge_v,bleu_m,bleu,bleu_f;
vert_e:=(0,0.790002,0.340007);
turquoise:=(0.250999,0.878399,0.815699);
orange:=(0.589999,0.269997,0.080004);
vert_fonce:=(0,1.4*0.392193,0);
rose:=(1.0, 0.752907, 0.796106);
bleu_ciel:=(1.2*0.529405,1.2*0.807794,1);%.2*0.921598);
or:=(1,0.843104,0);
rouge_v:=(0.829997,0.099994,0.119999);
bleu_m:=(0.7*0.529405,0.7*0.807794,0.7);%*0.921598);
bleu_f:=(0.211762,0.3231176,0.3686392);
bleu:=(0.529405,0.807794,1);

%   ARCSIN  ARCCOS  ARCTAN

vardef sin(expr x) =
sind(x/Pi*180)
enddef;

vardef cos(expr x) =
cosd(x/Pi*180)
enddef;

vardef tan(expr x) =
sin(x)/cos(x)
enddef;

beginfig(1);
pair O,A[],B[],P,Q,M[],T[],X[],Y[];
path p[], axex,axey, droite;
picture figure;
numeric u,rayon,pi;
u=3cm;
rayon=1.5u;
pi=3.1419;
O=(0,0); A1 = (-1.1*pi*u/2,0); A2 =(1.1*pi*u/2,0);
axex = A1--A2;
drawarrow axex withpen pencircle scaled 1.2bp;
label.urt(btex $x$ etex, A2);
B1 = (0,-2u); B2 =(0,2u);
axey = B1--B2;
drawarrow axey withpen pencircle scaled 1.2bp;
label.ulft(btex $y$ etex, B2);
p6 = (-pi*u/2,u*sind(-90))%{dir(cosd(i))}
for i=-89 upto 90: ..(i*pi*u/180,u*sind(i)){dir(cosd(i))} endfor;
draw p6  withpen pencircle scaled 2bp withcolor vert_e;
droite=(-pi*u/2,-pi*u/2)--(pi*u/2,pi*u/2);
draw droite withcolor red dashed withdots withpen pencircle scaled 2bp;
p7 = p6reflectedabout ((-pi*u/2,-pi*u/2),(pi*u/2,pi*u/2));
draw p7 withcolor bleu_m   withpen pencircle scaled 3bp;

%graduation de l'axe y
dotlabel.ulft(btex  $0$ etex ,(0,0));
dotlabel.lft(btex $1$ etex,(0,1u));
dotlabel.ulft(btex $\dfrac{\pi}{2}$ etex ,(0,pi*u/2));
dotlabel.lft(btex $-1$ etex ,(0,-1u));
dotlabel.llft(btex$-\dfrac{\pi}{2}$ etex ,(0,-pi*u/2));

%graduation de l'axe x
dotlabel.bot(btex  $0$ etex ,(0,0));
dotlabel.lrt(btex $1$ etex,(1u,0));
dotlabel.bot(btex $\dfrac{\pi}{2}$ etex ,(pi*u/2,0));
dotlabel.llft(btex $-1$ etex ,(-1u,0));
dotlabel.bot(btex $-\dfrac{\pi}{2}$ etex ,(-pi*u/2,0));

P = ((2.5*pi/6)*u, sind((2.5*180)/6)*u);
label.bot(btex $\sin x$etex, P);
Q = P reflectedabout ((0,0),(pi*u,pi*u));
label.lft(btex$\arcsin x$ etex, Q);

draw (-u, -pi*u/2)--(u,-pi*u/2)--(u,pi*u/2)--(-u,pi*u/2)--cycle withcolor bleu;
endfig;

beginfig(2);
pair O,A[],B[],P,Q,M[],T[],X[],Y[];
path p[], axex,axey, droite;
picture figure;
numeric u,rayon,pi;
u=3cm;
rayon=1.5u;
pi=3.1419;
O=(0,0);
label.llft(btex $O$ etex, O);
A1=(-1.1u,0);
A2=(1.1*pi*u,0);
axex=A1--A2;
drawarrow axex withpen pencircle scaled 1.2bp;
label.urt(btex $x$ etex, A2);
B1=(0,-1.2u);
B2=(0,1.1*pi*u);
axey = B1--B2;
drawarrow axey withpen pencircle scaled 1.2bp;
label.ulft(btex $y$ etex, B2);
p6 =(0*u,cosd(0)*u){dir(-sind(0))} for i=1 upto 180:
..(i*(pi/180)*u,u*cosd(i)){dir(-sind(i))} endfor;
draw p6 withpen pencircle scaled 2bp withcolor vert_e;
droite =(0,0)--(pi*u,pi*u);
draw droite withcolor red dashed withdots withpen pencircle scaled 2bp;
p7= p6 reflectedabout ((0,0),(pi*u,pi*u));
draw p7 withcolor bleu_m   withpen pencircle scaled 3bp ;

dotlabel.lft(btex $-1$ etex,(0,-1u));
dotlabel.lft(btex $-0,5$ etex,(0,-.5u));
dotlabel.ulft(btex  $0$ etex,(0,0));
dotlabel.lft(btex $0,5$ etex,(0,0.5u));
dotlabel.lft(btex $1$ etex,(0,1u));
dotlabel.urt(btex $\dfrac{\pi}{2}$ etex ,(0,pi*u/2));
dotlabel.ulft(btex $\pi$ etex ,(0,pi*u));

dotlabel.bot(btex $-1$ etex, (-1u,0));
dotlabel.bot(btex $1$ etex, (1u,0));
dotlabel.bot(btex $\dfrac{\pi}{2}$ etex, (pi*u/2,0));
dotlabel.bot(btex $\pi$ etex, (pi*u,0));

P = ((2.5*pi/6)*u, cosd((2.5*180)/6)*u);
label.urt(btex $\cos x$ etex, P);
Q = P reflectedabout ((0,0),(pi*u,pi*u));
label.urt(btex $\arccos x$ etex, Q);
draw (-u, 0)--(-u,pi*u)--(u,pi*u)--(u,0) withcolor bleu;
endfig;

beginfig(3);
pair O,A[],B[],P,Q,M[],T[],X[],Y[];
path p[], axex, axey, droite;
picture figure;
numeric u,rayon,pi;
u=2cm;
rayon=1.5u;
pi=3.1419;
O=(0,0);
label.llft(btex $O$ etex, O);
A1=(-1.1*pi*u,0);
A2=(1.1*pi*u,0);
axex=A1--A2;
drawarrow axex withpen pencircle scaled 1.2bp;
draw axex shifted (0,pi*u/2)withcolor bleu;
draw axex shifted (0,-pi*u/2)withcolor bleu;
label.urt(btex $x$ etex, A2);
B1=(0,-1.1*pi*u);
B2=(0,1.1*pi*u);
axey= B1--B2;
drawarrow axey withpen pencircle scaled 1.2bp;
draw axey shifted (pi*u/2,0) withcolor bleu;
draw axey shifted (-pi*u/2,0)withcolor bleu;

label.ulft(btex $y$ etex, B2);
p6 = (-75*(pi/180)*u,(sind(-75)/cosd(-75))*u)%{dir(-sind(-89))}
for i=-74 upto 75:
..(i*(pi/180)*u,(sind(i)/cosd(i))*u)%{dir(-sind(i))}
endfor;
draw p6  withpen pencircle scaled 2bp withcolor vert_e;
droite=(-pi*u,-pi*u)--(pi*u,pi*u);
draw droite withcolor red dashed withdots withpen pencircle scaled 2bp;
draw p7 withcolor bleu_m   withpen pencircle scaled 3bp ;

dotlabel.llft(btex $-\pi$ etex ,(0,-pi*u));
dotlabel.lft(btex $-3$ etex ,(0,-3u));
dotlabel.llft(btex $-2$ etex ,(0,-2u));
dotlabel.lft(btex $-1$ etex ,(0,-1u));
dotlabel.llft(btex $-\dfrac{\pi}{2}$ etex ,(0,-pi*u/2));
dotlabel.lft(btex $-0,5$ etex,(0,-.5u));
dotlabel.ulft(btex  $0$ etex ,(0,0));
dotlabel.lft(btex $1$ etex ,(0,1u));
dotlabel.ulft(btex $\dfrac{\pi}{2}$ etex,(0,pi*u/2));
dotlabel.ulft(btex $2$ etex ,(0,2u));
dotlabel.lft(btex $3$ etex ,(0,3u));
dotlabel.ulft(btex $\pi$ etex,(0,pi*u));

dotlabel.llft(btex $-\pi$ etex, (-pi*u,0));
dotlabel.bot(btex $-3$ etex, (-3u,0));
dotlabel.llft(btex $-2$ etex, (-2u,0));
dotlabel.llft(btex $-\dfrac{\pi}{2}$ etex, (-pi*u/2,0));
dotlabel.bot(btex $-1$ etex, (-1u,0));
dotlabel.bot(btex $1$ etex, (1u,0));
dotlabel.llft(btex $\dfrac{\pi}{2}$ etex,(pi*u/2,0));
dotlabel.bot(btex 2 etex, (2u,0));
dotlabel.bot(btex  $3$  etex, (3u,0));
dotlabel.lrt(btex $\pi$ etex,(pi*u,0));

P = ((pi/4)*u, (sind(180/4)/cosd(180/4))*u);
label.ulft(btex $\tan x$ etex, P);
Q = P reflectedabout ((0,0),(pi*u,pi*u));
label.lrt(btex  $\arctan x$ etex, Q);
endfig;
end