Basic Sampling Question: Understanding Frequency Change in Piecewise Sinusoid

[CoolDude420]

Homework Statement

Hi, I have the following continuous sinusoid given by

Now, if I sample this with a sampling rate of $$f_s = 4f_0$$

, I am told this is the answer,

I don't understand that. How come the frequency of the sinusoid has changed? I already studied sampling, etc. but this is the first time I've come across it in a piecewise manner like this. I can't seem to understand what just happened?

Homework Equations

The Attempt at a Solution

 

[boneh3ad]

The frequency hasn't changed. The coefficient inside has changed because your independent variable is no longer time, but $n$. Try coming up with $n$ as a function of $f_0$ and $t$ and see what you get.