I am not sure I understand. Sin(x) approaches x only when x approaches 0. When else does the universe does a bad job with this approximation?
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the joke is that sometimes the universe is bad at making sure x always approaches 0.
sin(x)=x in the same way that c=π=1 when doing cosmology.
At least you can often recover the constants after the fact with dimensional analysis in cosmology =P
1=c=G=hbar and sometimes =k is not even a joke, that's just natural units. Pi=e=1 however ... is only half a joke, because cosmologists are often only interested in orders of magnitudes, and even those are sometimes approximated.