Verified answer

The amplitude is 1, and the period is 2π/6 = π/3.

So the x-intercepts are ± π/3, ± 2π/3, etc.

The y-intercept is 1.

I would divide the interval from x = 0 to x = π/3 into 4 subintervals: 0, π/12, π/6, π/3.

The curve starts at (0, 1), then goes down to (π/12, 0), down more to (π/6, -1), then back up to the x-axis at (π/3, 0). Repeat that pattern.

y=cos 6x

first of all define the interval if it is e.g -30degress to 30 degress

the put x=0, 5,10, 15, 20, 25, 30 and vice versa x=0, -5,-10, -15,- 20,- 25, -30

you will get 6x= 0, 30, 60, 90, 120, 150, 180 degrees take cos 6x on the x-axis and by calculating y plot it on graph

the value of cos is always between -1 and 1 so the graph will be between y=-1 and y=1

and the line will be decresing from point (0,1) towards the positive side and the negative side to (-1/2,-1) and (1/2,-1) then upward to (1,1) and (-1,1) then goes down again and so on

it will look just like y = cos x, except that the period will be 2pi/6 = pi/3, instead of 2pi

the max will be at 0 and pi/3

the min will be at pi/6

zeros will be at pi/12 and 3pi/12 = pi/4

then repeat this pattern every pi/3

there will be 6 complete cycles in an interval of 2pi