import graph_pi;

unitsize(x=2cm,y=4cm);
real f(real x){return abs(sin(x));};
real g(real x){return cos(x);};
real x;

xlimits(-.25, 8);
ylimits(-1.25, 1.25);
xaxis(LeftTicks);
yaxis(Ticks);
path Cf=graph(f, 0, 8,500);
path Cg=graph(g, 0, 8,500);
draw(Cf,bp+red);
draw(Cg,bp+blue);

x=pi/4;
/*MODgraph_pi.asy.html#addtangentMOD*/
addtangent(Cf, x, .5yellow, drawleft=false);
addtangent(Cg, x, .5yellow, drawright=false);
dot((x,f(x))^^(x,g(x)));

x=3*pi/4;
path tg=tangent(Cf, x);
draw(tg);
addtangent(Cg, x);
pair M=intersectionpoint(tg,Cg);
dot("$M$",M,E);
addtangent(Cg, M.x, size=3cm,p=red);
draw((x,f(x))--(x,g(x)),scale(2)*MarkFill[0]);

x=pi;
addtangent(Cg, x, size=2cm,.8(green+blue));
dot((x,g(x)));

x=5*pi/4;
addtangent(Cf, x, size=2cm, v=(1,.25/sin(x)),
            drawright=false, p=red, arrow=Arrow(5mm,NoFill));
addtangent(Cf, x, size=2cm, drawleft=false, red);
dot((x,f(x)));

x=2*pi;
addtangent(Cf, x, size=4cm,p=.8green,differentiable=false);
dot((x,f(x)));