How do you graph #y=2cos6pix#?

1 Answer

#y=2cos6pix#
Considering the salient points,

At #cos6pix=0;#
y=0,
when #2cos6pix=0#
when#cos6pix=0#
when#6pix=(-7pi)/2,(-5pi)/12,(-3pi)/12, (-pi)/12,pi/2,(3pi)/2,(5pi)/2,(7pi)/2,...#
#x=...-7/12,-5/12,-3/12,-1/12,1/12,3/12,5/12,7/12,...#

At #cos6pix=1;#
#y=2xx1=2#,
when#6pix=...,-8pi,-6pi,-4pi,+2pi,0,2pi,4pi,6pi,8pi,....#
#x=...,-4/3,-3/3,-2/3,-1/3,0,1/3,2/3,3/3,4/3,....#
#x=...,-16/12,-12/12,-8/12,0,4/12,8/12,12/12,16/12,...#

At #cos6pix=-1;#
#y=2 xx -1=-2#
2hen #6pix=...,-7pi,-5pi,-3pi,-pi,pi,3pi,5pi,7pi,....#
#x=...,-7/6,-5/6,-3/6,-1/6,1/6,3/6,5/6,7/6,....#
#x=...,-14/12,-10/12,-6/12,-2/12,2/12,6/12,10/12,14/12,....#

We have a family of points;
#x=...-7/12,-5/12,-3/12,-1/12,1/12,3/12,5/12,7/12,...# where #y=0#
#x=...,-16/12,-12/12,-8/12,-4/12,0,4/12,8/12,12/12,16/12,...# where #y=1#
#x=...,-14/12,-10/12,-6/12,-2/12,2/12,6/12,10/12,14/12,...# where #y=-1#