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David, your boldface strikes me as slightly disproportionate to the point being made. If the cosine is interpreted as a map $\mathbb{R} \to [0, 1]$, then section is perfectly appropriate. If on the other hand you mean to interpret cosine as a function $\mathbb{R} \to \mathbb{R}$, and if local section refers to a map whose domain is open, then technically this edit seems slightly wrong. :-)
Yeah, I guess it was just meant to indicate the added adjective, but now that you mention it, I retract my edit.
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