How do you use transformation to graph the cosine function and determine the amplitude and period of #y=3cosx#?

1 Answer
KillerBunny
May 6, 2018

The amplitude is #3# and the period is #2pi#

Explanation:

The most general cosine-like function that you can have is

#Acos(\omega x + phi) + b#

where:

  • #A#, as a multiplicative factor, affects the amplitude of the wave. The amplitude is exactly #A#.
  • #omega# affects the period of the wave. The period is #(2pi)/omega#.
  • #phi# is the shift of the wave. It affects the wave by horizontal translation.
  • #b# is also a shift, but vertical.

If we want to have

#Acos(\omega x + phi) + b = 3cos(x)#

it means that we have chosen #A=3#, #omega = 1#. #phi=0# and #beta=0#.

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