In steps how do you go from:

y = 25cos pi/200x + 30 to get the answer 44.695

That depends. Do you want an x that gives y=44.695? That woul dbe more interesting than evaluating y when x = 44.695.

So, the steps are:

y = 25cos π/200 x + 30
44.695 = 25cos π/200 x + 30
14.695 = 25 cos π/200 x
0.5878 = cos π/200 x
cos-1 .5878 = π/200 x
.9425 = π/200x = .0157x
x = 60