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  |cos x| = COS X  if  -π/2 <= x <= π/2         
          = - COS X if π/2 <= x <= 3π/2 
  in one period of 2 Pi.

Modulus means that the result of applying modulus is always positive. We are interested in the numerical value of the function inside but not whether it is positive or negative.  On the graph it is always above X axis only.  Any portion which is below x axis is reflected like image  to above x axis.

  | 3 | = 3      | -2 | = 2      | 0 |  = 0        | x/y | =  | x |  /  | y |
  for example log function is not defined for -ve values.  So we can say  y = log | x |    y  =  | x |  can also be defined as 
       y =    x    if  x >=  0
             - x      if  x < 0       As  -x is positive for x<0, we get  y positive.

Look at the enclosed files.     
The graph between  x = 90 deg  and 270 deg is  reflected to above x axis as if the is a mirror on x axis.

the answer if you like it - please mark it as brainliest answer. rate the answer
We knw that |cos(x)|=1 if x=0 =-1 if x=180
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