Question

How do you graph `y=2cos6pix`?

Answer 1

`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`