# Question #576a4

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:

$y = \cos \left(x\right)$

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:

$y = A \cos \left(\omega \cdot x - \phi\right) + C$

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:

$f \left(x\right) = 2 \cos \left(x\right) - 2$

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