find the value of x

cos(3x)= -0.419 for 0<x<270

I do arc cos -0.419 which equals 114.77

and then to find the second angle in the 3rd quadrant

why do I need to minus 360 to get the degree in the 3rd quadrant?

why not add 90 to 114.77 to make it in the 3rd quadrant?

someone please explain this