# source("http://macosa.dima.unige.it/r.R")
f <- function(x) sin(3*x-pi/6); g <- function(x) sin(2*x)
BF=6; HF=2
TICKx=pi/4; TICKy=1/2; a=-pi/2; b=2.5*pi
Plane2(a,b, -1,1)
graph1(f,a,b, "brown"); graph1(g,a,b, "seagreen")
underX("pi",pi); underX("0",0); underX("2pi",2*pi)
underY("-1",-1); underY("1",1); underY("0",0)
line(0,1.05, 2*pi,1.05, "blue")

  
#
BF=4; HF=3
a=0; b=pi/2; TICKx=pi/6; TICKy=1/2; Plane2(a,b, 0,1)
graph1(f,a,b, "brown"); graph1(g,a,b, "seagreen")
underX("pi/2",pi/2); underX("0",0)
underY("-1",-1); underY("1",1); underY("0",0)
underX("0.4",0.4); underX("0.8",0.8); underX("1.2",1.2)
h=solution2(f,g, 0.4,0.6); h
# 0.5235988
k=solution2(f,g, 0.6,0.8); k
# 0.7330383
fraction(h/pi); fraction(k/pi)
# 1/6    7/30      quindi h=pi/6  k=pi*7/30
Point(h,f(h),"red"); Point(k,f(k),"red")

              
#
# Tutte le soluzioni (rifaccio il grafico iniziale):
BF=6; HF=2
TICKx=pi/4; TICKy=1/2; a=-pi/2; b=2.5*pi
Plane2(a,b, -1,1)
graph1(f,a,b, "brown"); graph1(g,a,b, "seagreen")
underX("pi",pi); underX("0",0); underX("2pi",2*pi)
underY("-1",-1); underY("1",1); underY("0",0)
# poi:
h=solution2(f,g, 0.4,0.6); fraction(h/pi); Point(h,f(h),"red")
# 1/6   [*pi]
k=solution2(f,g, 0.6,0.8); fraction(k/pi); Point(k,f(k),"red")
# 7/30  [*pi]
u=solution2(f,g, pi/2,pi); fraction(u/pi); Point(u,f(u),"red") 
# 19/30 [*pi]
v=solution2(f,g, pi,pi+pi/4); fraction(v/pi); Point(v,f(v),"red")
# 31/30 [*pi]
w=solution2(f,g, pi+pi/4,pi+pi/2); fraction(w/pi); Point(w,f(w),"red")
# 43/30 [*pi]
z=solution2(f,g, pi+pi/2,2*pi); fraction(z/pi); Point(z,f(z),"red")
# 11/6  [*pi]