Which of the following are equivalent to the function y=4cos(x-2)

Question

Answer 1

I think that you mean y = 4cosx - 2, not cos(x - 2)

Since y = cosx is an even function, cos(-x) = cosx. So, 4cos(-x) - 2 = 4cosx - 2

4sin(x + π/2) - 2 = 4[sinxcos(π/2) + cosxsin(π/2)] - 2 = 4cosx - 2

Another way of looking at this is to notice that the graph of y = sin(x + π/2) can be obtained by translating the graph of y = sinx π/2 units to the left, which coincides with the graph of y = cosx.