Question #576a4

1 Answer
David B.
Jul 13, 2016

No, there is no phase shift, although there is an offset and magnitude.

Explanation:

The most common reference sinusoid function is the #cos# function:

#y=cos(x)#

graph{cos(x) [-10, 10, -2, 2]}

We should be able to generate any general oscillation using this function by adding some change to one or more of the parameters. The full parameterization of the #cos# function can be written as:

#y= A cos (omega*x - phi) + C#

where
#A# is the amplitude
#omega# is the angular frequency
#phi# is the phase shift
and #C# is the offset

Let's take an example where we have changed some of these parameters:

#A=0.5#
#omega=2#
#phi = 1#
#C=1#

Looking at the formula that we were given:

#f(x) = 2 cos(x) -2#

we can see that there is a change in amplitude, and an offset, but no change in frequency or phase.

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