%@AUTEUR: Pierre Fournier 

verbatimtex
%&latex
\documentclass{article}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{palatino}
\usepackage{amsmath}
\begin{document}
etex;

input marith;

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 1.2bp;
droite =(-pi*u/2,-pi*u/2)--(pi*u/2,pi*u/2);
draw droite;
p7 = p6 reflectedabout ((-pi*u/2,-pi*u/2),(pi*u/2,pi*u/2));
draw p7 dashed evenly withpen pencircle scaled 1.2bp;

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

%graduation de l'axe x

dotlabel.bot(btex  $0$ etex ,(0,0));
dotlabel.bot(btex $1$ etex ,(1u,0));
dotlabel.bot(btex $\dfrac{\pi}{2}$ etex ,(pi*u/2,0));
dotlabel.bot(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);
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 1.2bp;
droite =(0,0)--(pi*u,pi*u);
draw droite;
p7 = p6 reflectedabout ((0,0),(pi*u,pi*u));
draw p7 dashed evenly withpen pencircle scaled 1.2bp;


%Graduation axe y
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.lft(btex $\dfrac{\pi}{2}$ etex ,(0,pi*u/2));
dotlabel.lft(btex $\pi$ etex ,(0,pi*u));

%Graduation axe x
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);

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);
draw axex shifted (0,-pi*u/2);
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);
draw axey shifted (-pi*u/2,0);

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 1.2bp;
droite =(-pi*u,-pi*u)--(pi*u,pi*u);
draw droite;
p7 = p6 reflectedabout ((-pi*u,-pi*u),(pi*u,pi*u));
draw p7 dashed evenly withpen pencircle scaled 1.2bp;


%Graduation axe y
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));

%Graduation axe x
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