How do you determine the amplitude, period and vertical translation of y + 2 = 4 cos ⁡ ( x 2 )?

Question

How do you determine the amplitude, period and vertical translation of   y  +  2  =  4  cos  ⁡  (      x    2    )?

Cheyanne Charles · Accepted Answer

I would write your function isolating y as:  y  =  4  cos  ⁡  (      x    2    )  −  2From this you can &quot;see&quot;:1] The amplitude of your cosine is 4 (the number in front of   cos);2] The period is   4  π ; by using the       1    2   inside the argument of   cos you get:  p  e  r  i  o  d  =            2      π              1      2        =  4  π3] The vertical translation is given by -2 telling you that your   cos oscillates about the horizontal line passing through y=-2 (instead of oscillating about the x axis).Graphically:graph{  4  cos  ⁡  (  x      /    2  )  −  2  [  −  16.02  ,  16.02  ,  −  8.01  ,  8.01  ]}As you can see you have a cosine oscillating between 2 and -6 about the horizontal line at y=-2 and one complete oscillation now takes   4  π to be completed.

How do you determine the amplitude, period and vertical translation of y+2=4cos(x/2)

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