It's rumoured they'll also endorse function for mathematicians (6)

I believe the answer is:

cosine

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'function for mathematicians' is the definition.
'cosine' can be an answer for 'function' (mathematical function). I'm not certain of the 'for mathematicians' bit.

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for cosine that I've seen before include "Trig function" , "Ratio in trigonometry" , "Trigonometrical ratio" , "Trigonometric function" , "Trig ratio" .)

I've seen this clue in The Irish Times.

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