code for diagram

> grph:=plot(sin(x),x=-Pi..Pi,thickness=3):
dsk1:=plottools[disk]( [-Pi/2,-1],.07 ,color=blue):
dsk2:=plottools[disk]( [pt,sin(pt)],.07 ,color=blue):

> eq:=-1 = cos(q)*(-Pi/2 -q)+sin(q):

> pt:=fsolve(eq,q,0..3);
lineq:=-1+cos(pt)*(x+Pi/2);

> lne:=plot(lineq,x=-Pi..Pi/2,thickness=2):
txt:=plots[textplot]({[-Pi/2.0,-1.6,`( -Pi/2, -1
)`],[pt,sin(pt)+.4,`?`]},font=[TIMES,BOLD,16]):

> plots[display]({lne,grph,txt,dsk1,dsk2},xtickmarks=[],
ytickmarks=[],scaling=constrained);