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.

Related questions
See all questions in Amplitude, Period and Frequency
Impact of this question
1431 views around the world
You can reuse this answer
Creative Commons License