!set n=$counter
rounding=0
!readproc $remarkdir/rounding.$taal
checkfile=exos/checkfile7.proc
math=1
colls=20
rows=5
questiontype=0
!if $level=0
    R=$counter
!else
    R=$level
!endif        
woordmax=150
charmax=300

ss=!record 63 of lang/remarks.$taal
#@ Los exact op:
question$n=$ss
keuze=!randitem 1,0
!if $R=1
    domein=-6:6
    !if $keuze=1
	a=!randitem 3,4,5,6,7,8,9
	functie2=sin($a*x)
	functie1=2*sin(x)*cos(x)
	answer$n=k*2*pi/($a-2),pi/($a+2)+k*2*pi/($a+2)
	var5=2
	var4=2
	texanswer$n= x_1=\left[ \begin{array}{l} \frac{2k\cdot \pi}{$[($a-2)]} \\ x_2=\frac{\pi}{$[($a+2)]} + \frac{2k\cdot \pi}{$[($a+2)]} \end{array} \right.
	# var5= was "$gi" aantal goede antwoorden
    !else    
	a=!randitem 1,sqrt(3),sqrt(2)
	functie1=sin(2*x)
	functie2=$a*cos(x)
	!if $a=1
	    answer$n=1/2*pi+k*pi,1/6*pi+k*2*pi,5/6*pi+k*2*pi
	    G1=\frac{\pi}{2} + k\cdot \pi
	    G2=\frac{\pi}{6} + 2k\cdot \pi
	    G3=\frac{5\cdot \pi}{6} + 2k\cdot \pi
	!else
	    !if $a=sqrt(3)
		answer$n=1/2*pi+k*pi,1/3*pi+k*2*pi,2/3*pi+k*2*pi
		G1=\frac{\pi}{2} + 2k\cdot \pi
		G2=\frac{\pi}{3} + 2k\cdot \pi
		G3=\frac{2\cdot \pi}{3} + 2k\cdot \pi
	    !else
		answer$n=1/2*pi+k*pi,1/4*pi+k*2*pi,3/4*pi+k*2*pi
		G1=\frac{\pi}{2} + 2k\cdot \pi
		G2=\frac{\pi}{4} + 2k\cdot \pi
		G3=\frac{3\cdot \pi}{4} + 2k\cdot \pi
	    !endif
	!endif
	texanswer$n=\left [ \begin{array}{l} x_1=$G1 \\ x_2=$G2 \\ x_3=$G3 \end{array}\right.
	var5=3
	var4=3
    !endif
    formula$n=!texmath $functie2 = $functie1
!endif 

!if $R>1
    domein=-6:6
    !if $keuze=1
	ch=!randitem 1,2,3,4
	k1=1,1/2,1/2*sqrt(2),1/2*sqrt(3)
	k2=1,\frac{1}{2},\frac{1}{2} \cdot \sqrt{2},\frac{1}{2} \cdot \sqrt{3}
	a=!item $ch of $k1
	atex=!item $ch of $k2
	functie1=(cos(x))^2 - (sin(x))^2
	functie2=$a
	formula$n=\cos^{2}\left( x \right) - \sin^{2}\left( x \right) = $atex
	!if $a=1
	    answer$n=k*pi
	    var5=1
	    var4=1
	    texanswer$n= k\cdot \pi
	!else
	    !if $a=1/2
		answer$n=1/6*pi+k*pi,-1/6*pi+k*pi,5/6*pi+k*pi
		# let op cos geeft 2 setjes
		G1=\frac{\pi}{6} + k\cdot \pi
		G2=\frac{-\pi}{6} + k\cdot \pi
		G3=\frac{5\cdot \pi}{6} + k\cdot \pi
		var5=3
		var4=2
	    !else
		!if $a=1/2*sqrt(2)
		    answer$n=1/8*pi+k*pi,-1/8*pi+k*pi,7/8*pi+k*pi	
		    var5=3
		    var4=2
		    G1=\frac{\pi}{8}+k\cdot \pi
		    G2=\frac{-\pi}{8}+k\cdot \pi
		    G3=\frac{7 \cdot \pi}{8}+k\cdot \pi		    
	    	!else
		    answer$n=1/12*pi+k*pi,-1/12*pi+k*pi,11/12*pi+k*pi	
		    var5=3
		    var4=2
		    G1=\frac{\pi}{12} + k\cdot \pi
		    G2=\frac{-\pi}{12} + k\cdot \pi
		    G3=\frac{11\cdot \pi}{12} + k\cdot \pi
		!endif
		texanswer$n=\left[ \begin{array}{l} x_1=$G1 \\ x_2=$G2 \end{array}\right.
	    !endif
	!endif    
    !else    
	a=!randitem 3,4,5,6,7,8,9
	functie1=cos($a*x)
	functie2=(cos(x))^2 - (sin(x))^2
	answer$n=k*2*pi/($a-2),k*2*pi/($a+2),2*pi/($a+2)+k*2*pi/($a+2)
	formula$n=\cos\left( $a \cdoy x \right) \,\, =\,\, \cos^{2}\left( x \right) - \sin^{2}\left( x \right)
	var5=3
	var4=2
	G1=2k \cdot \frac{pi}{$[($a-2)]}
	G2=2k \cdot \frac{pi}{$[($a+2)]}
	texanswer$n=\left[ \begin{array}{l} x_1=$G1 \\ x_2=$G2 \end{array}\right.
    !endif
!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] $functie1 notitle ,$functie2 notitle
!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] $functie1,$functie2 notitle

	helptext=!record 63 of $remarkdir/commonremarks.$taal
	helptext=<a href="javascript:showimage();">$helptext
    !endif
!endif
