Here we see cosines of various frequencies sampled at eight points.
The lowest frequency, zero hertz (DC), is indicated in red,
for which the samples produce
identical values.
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The next highest frequency, 1 cycle, is shown in orange.
this would be one Hertz if
the total duration of the sample was one second (i.e. if the sampling
frequency were 8 Hertz).  The yellow plot denotes 2 Hertz, green
denotes 3 Hertz, and blue denotes 4 Hertz.  (The blue 4Hz
plot is right at the Nyquist frequency,
i.e. exactly half the samping rate.)
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<img src=sampledcosines.gif>
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Finally, we see the variously sampled cosines together in the same plot
(color coded in order of frequency as red, orange, yellow, green, blue).
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If we continue to raise the frequency, we get aliasing, e.g.
if we make five cycles of the cosine in 1 second (8 samples),
we get a frequency of 5 Hertz (fractional frequency is 5/8),
and this produces the same samples as the samples of the 3 Hertz
sinewave.