Contrast those with the following sentences, none of which contains a copula:
The 'is' in the first sentence is an auxiliary verb: the main verb is 'tapping'.
'Looks' and 'appears' are action verbs in these cases.
Phil is tapping his fingers.
Sally looks speculatively at Phil.
The walrus appears in the middle of the room in a puff of smoke.
Some languages do not have a copula. as a matter of fact, some varieties of English lack a copula. In these varieties, you can grammatically say:
Phil just a mellow dude.
Really, why bother with an equals sign when it's pretty clear what the sentence means without it? That silly.
La mors-a alt-a mir-a a lo-s human-o-s cort-o-s.
DEF walrus-F tall-F look-3 PARTICLE DEF-PL human-M-PL short-M-PL
The tall walrus looks at the short humans.
Notice also, once again, that there is information in the glosses that doesn't make it to the translation.
verb shorten (adding the idea 'to make' so this means 'make short'.
adj ttestable (adding the idea 'be able to')
noun farmer (adding the idea person)
These last two are interesting because the affixes are homophones with other affixes. Yes, there is a derivational -er that means 'person who' and changes a verb to a noun besides. There is also an -er that is inflectional: it's the comparative: red vs. redder. Similarly, the -ing on 'offering' can have two meanings. It might be inflectional, adding the idea of present continuous to a verb as in the first sentence below. It can also turn that verb into a noun as in the second sentence below. (Can you think of a word in which the suffix -s is derivational? It's usually an inflectional suffix meaning plural or possession.)
Phil is offering Sally a flower.
The offering makes her smile.
You often have to look at how a word functions in a sentence to know its part of speech. Here is the same form used as three different parts of speech.
Adj: The yellow flower is lovely.
Noun: Sally likes how the yellow reflects off Phil's glasses.
Verb: The walrus's tusks will certainly yellow as he ages.
So, you can change part of speech without adding an affix or modifying the word in any way. We call that 'zero derivation'.