Question #fa041

1 Answer
sente
Oct 14, 2016

#D = uuu_(n in ZZ)(2pin, pi+2pin)#

Explanation:

As sine is periodic with a period of #2pi# and is positive on #(0, pi)#, we have that #sinphi > 0 <=> phi in (2pin, pi+2pin)# for some #n in ZZ#.

Just like how we can use #sum# to denote repeated addition or #prod# to denote repeated multiplication, we can use #uuu# to denote repeated unions. Thus, to express the set of all values on which sine is positive, we can write it as the union of all intervals of the form #(2pin, pi+2pin)# for some integer #n#, i.e.

#D = uuu_(n in ZZ)(2pin, pi+2pin)#

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