Low Pass: Why did my professor use frequency and not angular frequency?

[space5678]

Homework Statement

We are given a passive RC low pass filter with an input voltage of 5 V_rms at a frequency of 1 kHz. The resistor has a value of 22 kΩ, the capacitor a value of 100 nF. There is a current i across the resistor. (see picture below)

We are to calculate the magnitude and phase angle of the output voltage.

By the way, in the picture below is in german, so V eff means rms, I think the rest should be apparent.

Homework Equations

U_R = R*I

U_out = I*X_C

X_C = I / ω*C

ω = 2*π*f (in rad/s)

The Attempt at a Solution

Analytically, this is not a problem, and I have attached the solution from the professor. My only problem is that for ω the professor used the frequency f, and not 2πf. As in:

ω = f = 1 kHz

This makes no sense to me and seems wrong. Could somebody possibly clarify what´s going on here? Thanks in advance.

 

[CWatters]

Seems wrong to me as well. I got 0.36V.

 

[space5678]

Seems wrong to me as well. I got 0.36V.

I think this must be a clerical mistake, as in all of the other examples he uses ω = 2πf. Thanks a bunch for checking!