Explanation:
I assume, based on what I see, that the solid line is just cos(x), right ?
and we need to find the equation that draws the dotted line, correct ?
the notation is strange, as it seems we need to find a multiplication factor for x in the cos function.
but there is no multiplication factor that moves the cosine wave by pi to the left or to the right (so that the max. happens, where originally the minimum happens, and vice versa).
so, we need to add (or subtract) pi in the cosine function.
the rest is clear :
the normal distance between min. and max. of the cosine function is 2 (between +1 and -1). the target is 4. so we need to multiply by 2.
and since the values of that function have to be between -4 and 0 (instead of -2 and +2), we have to subtract overall 2.
giving us the function :
y = 2×cos(pi + x) + -2