One period of a function of the form ya cos kxb is shown in

One period of a function of the form y=a cos k(x-b) is shown in the figure. Determine the function.

Highest occurs at pi/3 and 13pi/3
So, period = 12pi/3 or 4pi
And thus constant k = 2pi/period
k = 2pi/4pi
k = 1/2

And this is considering
y = Acos[k(x-b)]

Amplitude = (max - min)/2
A = (3 - (-3))/2
A = 6/2
A = 3

And is there a phase shift?
Yes, usually cos will have a max at 0
Here cos has a max at pi/3
So, shifted pi/3 rightward

So, we have :
y = 3cos(1/2(x - pi/3)) ----> ANS