rounding=0
!readproc $remarkdir/rounding.$taal
checkfile=exos/checkfile7.proc
cols=25
rows=5
mathview=0
math=1
questiontype=0
!set n=$counter
!if $level =0
    R=$counter
!else
    R=$level
!endif        
woordmax=150
charmax=300
# uitzetten...ivm 1 of 2 wortels
exotitle=!record 20 of lang/remarks.$taal
#@ Vergelijkingen en Goniometrie (type sin(ax+d) = c)
question$n=!record 63 of lang/remarks.$taal
#@ Los exact op:
keuze=!randitem 1,0
domein=-20:20
!if $R=1
    bereik=-1.5:1.5
    !if $keuze=1
	oplossingen=!randitem 0:1:k*pi,\
	1:1:1/2*pi+2*k*pi,\
	-1:1:3/2*pi+2*k*pi:-1/2*pi+2*k*pi,\
	1/2:2:1/6*pi+2*k*pi:5/6*pi+2*k*pi,\
	-1/2:2:7/6*pi+2*k*pi:11/6*pi+2*k*pi:-1/6*pi+2*k*pi:-5/6*pi+2*k*pi,\
	1/2*sqrt(2):2:1/4*pi+2*k*pi:3/4*pi+2*k*pi,\
	1/2*sqrt(3):2:1/3*pi+2*k*pi:2/3*pi+2*k*pi,\
	-1/2*sqrt(2):2:5/4*pi+2*k*pi:7/4*pi+2*k*pi:-1/4*pi+2*k*pi:-3/4*pi+2*k*pi,\
	-1/2*sqrt(3):2:4/3*pi+2*k*pi:5/3*pi+2*k*pi:-1/3*pi+2*k*pi:-2/3*pi+2*k*pi
	
	functie=sin(x)
	antwoord=!replace internal : by , in $oplossingen
	a=!item 1 of $antwoord
	formula$n=!texmath $functie = $a
    !else    
	oplossingen=!randitem 0:1:1/2*pi+k*pi,\
	1:1:2*k*pi,\
	-1:1:pi+2*k*pi:-1*pi+2*k*pi,\
	1/2:2:1/3*pi+2*k*pi:-1/3*pi+2*k*pi:5/3*pi+2*k*pi,\
	-1/2:2:2/3*pi+2*k*pi:-2/3*pi+2*k*pi:4/3*pi+2*k*pi,\
	1/2*sqrt(2):2:1/4*pi+2*k*pi:-1/4*pi+2*k*pi:7/4*pi+2*k*pi,\
	1/2*sqrt(3):2:1/6*pi+2*k*pi:-1/6*pi+2*k*pi:11/6*pi+2*k*pi,\
	-1/2*sqrt(2):2:3/4*pi+2*k*pi:-3/4*pi+2*k*pi:5/4*pi+2*k*pi,\
	-1/2*sqrt(3):2:5/6*pi+2*k*pi:-5/6*pi+2*k*pi:7/6*pi+2*k*pi

	functie=cos(x)
	antwoord=!replace internal : by , in $oplossingen
	a=!item 1 of $antwoord
	formula$n=!texmath $functie = $a
    !endif
    !goto READY
!endif 

!if $R=2
    bereik=-1.5:1.5 
    !if $keuze=1
	b=!randitem 2,3,4,5,6
	oplossingen=!randitem 0:1:(1/$b)*k*pi,\
	1:1:(1/($[$b*2]))*pi+(2/$b)*k*pi,\
	-1:1:(3/($[$b*2]))*pi+(2/$b)*k*pi:(-1/($[$b*2]))*pi+(2/$b)*k*pi,\
	1/2:2:(1/($[$b*6]))*pi+(2/$b)*k*pi:(5/($[$b*6]))*pi+(2/$b)*k*pi,\
	-1/2:2:(7/($[$b*6]))*pi+(2/$b)*k*pi:(11/($[$b*6]))*pi+(2/$b)*k*pi:(-1/($[$b*6]))*pi+(2/$b)*k*pi:(-5/($[$b*6]))*pi+(2/$b)*k*pi,\
	1/2*sqrt(2):2:(1/($[$b*4]))*pi+(2/$b)*k*pi:(3/($[$b*4]))*pi+(2/$b)*k*pi,\
	-1/2*sqrt(2):2:(5/($[$b*4]))*pi+(2/$b)*k*pi:(7/($[$b*4]))*pi+(2/$b)*k*pi:(-1/($[$b*4]))*pi+(2/$b)*k*pi:(-3/($[$b*4]))*pi+(2/$b)*k*pi,\
	1/2*sqrt(3):2:(1/($[$b*3]))*pi+(2/$b)*k*pi:(2/($[$b*3]))*pi+(2/$b)*k*pi,\
	-1/2*sqrt(3):2:(4/($[$b*3]))*pi+(2/$b)*k*pi:(5/($[$b*3]))*pi+(2/$b)*k*pi:(-1/($[$b*3]))*pi+(2/$b)*k*pi:(-2/($[$b*3]))*pi+(2/$b)*k*pi
    
	functie=sin($b*x)
	antwoord=!replace internal : by , in $oplossingen
	a=!item 1 of $antwoord
	formula$n=!texmath $functie = $a
    !else
	b=!randitem 2,3,4,5,6
	oplossingen=!randitem 0:1:(1/($[$b*2]))*pi+(1/$b)*k*pi,\
	1:1:(2/$b)*k*pi,\
	-1:1:(1/$b)*pi+(2/$b)*k*pi:(-1/$b)*pi+(2/$b)*k*pi,\
	1/2:2:(1/($[$b*3]))*pi+(2/$b)*k*pi:(-1/($[$b*3]))*pi+(2/$b)*k*pi:(5/($[$b*3]))*pi+(2/$b)*k*pi,\
	-1/2:2:(2/($[$b*3]))*pi+(2/$b)*k*pi:(-2/($[$b*3]))*pi+(2/$b)*k*pi:(4/($[$b*3]))*pi+(2/$b)*k*pi,\
	1/2*sqrt(2):2:(1/($[$b*4]))*pi+(2/$b)*k*pi:(-1/($[$b*4]))*pi+(2/$b)*k*pi:(7/($[$b*4]))*pi+(2/$b)*k*pi,\
	1/2*sqrt(3):2:(1/($[$b*6]))*pi+(2/$b)*k*pi:(-1/($[$b*6]))*pi+(2/$b)*k*pi:(11/($[$b*6]))*pi+(2/$b)*k*pi,\
	-1/2*sqrt(2):2:(3/($[$b*4]))*pi+(2/$b)*k*pi:(-3/($[$b*4]))*pi+(2/$b)*k*pi:(5/($[$b*4]))*pi+(2/$b)*k*pi,\
	-1/2*sqrt(3):2:(5/($[$b*6]))*pi+(2/$b)*k*pi:(-5/($[$b*6]))*pi+(2/$b)*k*pi:(7/($[$b*6]))*pi+(2/$b)*k*pi

	functie=cos($b*x)
	antwoord=!replace internal : by , in $oplossingen
	a=!item 1 of $antwoord
	formula$n=!texmath $functie = $a
    !endif
    !goto READY
!endif 

!if $R=3
    bereik=-1.5:1.5 
    !if $keuze=1
	b=!randitem 2,3,4,5,6
	c=!randitem 1,2,3,4
	d=$[$c*$b]
	oplossingen=!randitem 0:1:(1/$b)*k*pi+$c,\
	1:1:(1/($[$b*2]))*pi+(2/$b)*k*pi+$c,\
	-1:1:(3/($[$b*2]))*pi+(2/$b)*k*pi+$c:(-1/($[$b*2]))*pi+(2/$b)*k*pi+$c,\
	1/2:2:(1/($[$b*6]))*pi+(2/$b)*k*pi+$c:(5/($[$b*6]))*pi+(2/$b)*k*pi+$c,\
	-1/2:2:(7/($[$b*6]))*pi+(2/$b)*k*pi+$c:(11/($[$b*6]))*pi+(2/$b)*k*pi+$c:(-1/($[$b*6]))*pi+(2/$b)*k*pi+$c:(-5/($[$b*6]))*pi+(2/$b)*k*pi+$c,\
	1/2*sqrt(2):2:(1/($[$b*4]))*pi+(2/$b)*k*pi+$c:(3/($[$b*4]))*pi+(2/$b)*k*pi+$c,\
	-1/2*sqrt(2):2:(5/($[$b*4]))*pi+(2/$b)*k*pi+$c:(7/($[$b*4]))*pi+(2/$b)*k*pi+$c:(-1/($[$b*4]))*pi+(2/$b)*k*pi+$c:(-3/($[$b*4]))*pi+(2/$b)*k*pi+$c,\
	1/2*sqrt(3):2:(1/($[$b*3]))*pi+(2/$b)*k*pi+$c:(2/($[$b*3]))*pi+(2/$b)*k*pi+$c,\
	-1/2*sqrt(3):2:(4/($[$b*3]))*pi+(2/$b)*k*pi+$c:(5/($[$b*3]))*pi+(2/$b)*k*pi+$c:(-1/($[$b*3]))*pi+(2/$b)*k*pi+$c:(-2/($[$b*3]))*pi+(2/$b)*k*pi+$c
    
	functie=sin($b*x-$d)
	antwoord=!replace internal : by , in $oplossingen
	a=!item 1 of $antwoord
	formula$n=!texmath $functie = $a
    !else
	b=!randitem 2,3,4,5,6
	c=!randitem 1,2,3,4
	d=$[$c*$b]
	oplossingen=!randitem 0:1:(1/($[$b*2]))*pi+(1/$b)*k*pi+$c,\
	1:1:(2/$b)*k*pi+$c,\
	-1:1:(1/$b)*pi+(2/$b)*k*pi+$c:(-1/$b)*pi+(2/$b)*k*pi+$c,\
	1/2:2:(1/($[$b*3]))*pi+(2/$b)*k*pi+$c:(-1/($[$b*3]))*pi+(2/$b)*k*pi+$c:(5/($[$b*3]))*pi+(2/$b)*k*pi+$c,\
	-1/2:2:(2/($[$b*3]))*pi+(2/$b)*k*pi+$c:(-2/($[$b*3]))*pi+(2/$b)*k*pi+$c:(4/($[$b*3]))*pi+(2/$b)*k*pi+$c,\
	1/2*sqrt(2):2:(1/($[$b*4]))*pi+(2/$b)*k*pi+$c:(-1/($[$b*4]))*pi+(2/$b)*k*pi+$c:(7/($[$b*4]))*pi+(2/$b)*k*pi+$c,\
	1/2*sqrt(3):2:(1/($[$b*6]))*pi+(2/$b)*k*pi+$c:(-1/($[$b*6]))*pi+(2/$b)*k*pi+$c:(11/($[$b*6]))*pi+(2/$b)*k*pi+$c,\
	-1/2*sqrt(2):2:(3/($[$b*4]))*pi+(2/$b)*k*pi+$c:(-3/($[$b*4]))*pi+(2/$b)*k*pi+$c:(5/($[$b*4]))*pi+(2/$b)*k*pi+$c,\
	-1/2*sqrt(3):2:(5/($[$b*6]))*pi+(2/$b)*k*pi+$c:(-5/($[$b*6]))*pi+(2/$b)*k*pi+$c:(7/($[$b*6]))*pi+(2/$b)*k*pi+$c

	functie=cos($b*x-$d)
	antwoord=!replace internal : by , in $oplossingen
	a=!item 1 of $antwoord
	formula$n=!texmath $functie = $a
    !endif
    !goto READY
!endif

!if $R>3
    e=!randitem 2,3,4,5,6
    pm=!randitem 1,-1    
    bereik=$[-1*($e+1)]:$[$e+1] 
    e=$[$pm*$e]
    !if $keuze=1
	b=!randitem 2,3,4,5,6
	c=!randitem 1,2,3,4
	d=$[$c*$b]
	oplossingen=!randitem 0:1:(1/$b)*k*pi+$c,\
	$e:1(1/($[$b*2]))*pi+(2/$b)*k*pi+$c,\
	$[-1*$e]:1:(3/($[$b*2]))*pi+(2/$b)*k*pi+$c:(-1/($[$b*2]))*pi+(2/$b)*k*pi+$c,\
	$[1/2*$e]:2:(1/($[$b*6]))*pi+(2/$b)*k*pi+$c:(5/($[$b*6]))*pi+(2/$b)*k*pi+$c,\
	$[-1/2*$e]:2:(7/($[$b*6]))*pi+(2/$b)*k*pi+$c:(11/($[$b*6]))*pi+(2/$b)*k*pi+$c:(-1/($[$b*6]))*pi+(2/$b)*k*pi+$c:(-5/($[$b*6]))*pi+(2/$b)*k*pi+$c,\
	$[1/2*$e]*sqrt(2):2:(1/($[$b*4]))*pi+(2/$b)*k*pi+$c:(3/($[$b*4]))*pi+(2/$b)*k*pi+$c,\
	$[-1/2*$e]*sqrt(2):2:(5/($[$b*4]))*pi+(2/$b)*k*pi+$c:(7/($[$b*4]))*pi+(2/$b)*k*pi+$c:(-1/($[$b*4]))*pi+(2/$b)*k*pi+$c:(-3/($[$b*4]))*pi+(2/$b)*k*pi+$c,\
	$[1/2*$e]*sqrt(3):2:(1/($[$b*3]))*pi+(2/$b)*k*pi+$c:(2/($[$b*3]))*pi+(2/$b)*k*pi+$c,\
	$[-1/2*$e]*sqrt(3):2:(4/($[$b*3]))*pi+(2/$b)*k*pi+$c:(5/($[$b*3]))*pi+(2/$b)*k*pi+$c:(-1/($[$b*3]))*pi+(2/$b)*k*pi+$c:(-2/($[$b*3]))*pi+(2/$b)*k*pi+$c
    
	functie=$e*sin($b*x-$d)
	antwoord=!replace internal : by , in $oplossingen
	a=!item 1 of $antwoord
	formula$n=!texmath $functie = $a
    !else
	b=!randitem 2,3,4,5,6
	c=!randitem 1,2,3,4
	d=$[$c*$b]
	oplossingen=!randitem 0:1:(1/($[$b*2]))*pi+(1/$b)*k*pi+$c,\
	$e:1:(2/$b)*k*pi+$c,\
	$[-1*$e]:1:(1/$b)*pi+(2/$b)*k*pi+$c:(-1/$b)*pi+(2/$b)*k*pi+$c,\
	$[1/2*$e]:2:(1/($[$b*3]))*pi+(2/$b)*k*pi+$c:(-1/($[$b*3]))*pi+(2/$b)*k*pi+$c:(5/($[$b*3]))*pi+(2/$b)*k*pi+$c,\
	$[-1/2*$e]:2:(2/($[$b*3]))*pi+(2/$b)*k*pi+$c:(-2/($[$b*3]))*pi+(2/$b)*k*pi+$c:(4/($[$b*3]))*pi+(2/$b)*k*pi+$c,\
	$[1/2*$e]*sqrt(2):2:(1/($[$b*4]))*pi+(2/$b)*k*pi+$c:(-1/($[$b*4]))*pi+(2/$b)*k*pi+$c:(7/($[$b*4]))*pi+(2/$b)*k*pi+$c,\
	$[1/2*$e]*sqrt(3):2:(1/($[$b*6]))*pi+(2/$b)*k*pi+$c:(-1/($[$b*6]))*pi+(2/$b)*k*pi+$c:(11/($[$b*6]))*pi+(2/$b)*k*pi+$c,\
	$[-1/2*$e]*sqrt(2):2:(3/($[$b*4]))*pi+(2/$b)*k*pi+$c:(-3/($[$b*4]))*pi+(2/$b)*k*pi+$c:(5/($[$b*4]))*pi+(2/$b)*k*pi+$c,\
	$[-1/2*$e]*sqrt(3):2:(5/($[$b*6]))*pi+(2/$b)*k*pi+$c:(-5/($[$b*6]))*pi+(2/$b)*k*pi+$c:(7/($[$b*6]))*pi+(2/$b)*k*pi+$c

	functie=$e*cos($b*x-$d)
	antwoord=!replace internal : by , in $oplossingen
	a=!item 1 of $antwoord
	formula$n=!texmath $functie = $a
    !endif
!endif

:READY

var4=!item 2 of $antwoord
answer$n=!item 3 to -1 of $antwoord
var5=!itemcnt $(answer$n)
!if $var4=1
    texanswer$n=!item 3 of $antwoord
    texanswer$n=!texmath $(texanswer$n)
    texanswer$n= x\,=\, $(texanswer$n)
!else
    G1=!item 1 of $(answer$n)
    G2=!item 2 of $(answer$n)
    G1=!texmath $G1
    G2=!texmath $G2
    texanswer$n= \left[ \begin{array}{l} x_1=$G1 \\ \\ x_2=$G2 \end{array} \right.	
!endif    

!if $image=1
    plot=1
    draw=0
    image_settings$n=size 0.7,0.4; noborder ; zeroaxis linetype 3 ; tmargin 1 ; rmargin 1 ; grid xtics ytics mxtics
    image$n=[$domein] [$bereik] $functie,$a
!else
    !if $teaching=1
	insplot_set=size 1,0.5; noborder ; zeroaxis linetype 3 ; tmargin 1 ; rmargin 1 ; grid xtics ytics mxtics
	!insplot [$domein] [$bereik] $functie,$a
	helptext=!record 63 of $remarkdir/commonremarks.$taal
	helptext=<a href="javascript:showimage();">$helptext
    !endif
!endif
