who invented theory of sets, function,trigonometry,mathematical induction?

Answer 1

Sets - Venn introduced the Venn diagram in 1881, but Georg Cantor is credited as the inventor of Set Theory.

The term "Function" was coined by Gottfried Leibniz in 1694

Trigonometry was known in antiquity by the Greeks and Arabs. Wiki says the Ancient Egyptians knew some trigonometry earlier than 2000BC