book . ▁In ▁the ▁case ▁of ▁music ▁theory , ▁the ▁application ▁of ▁trig on ometry ▁is ▁related ▁to ▁work ▁begun ▁by ▁P yth ag or as , ▁who ▁observed ▁that ▁the ▁sounds ▁made ▁by ▁pl uck ing ▁two ▁strings ▁of ▁different ▁lengths ▁are ▁con son ant ▁if ▁both ▁lengths ▁are ▁small ▁integer ▁multi ples ▁of ▁a ▁common ▁length . ▁The ▁res embl ance ▁between ▁the ▁shape ▁of ▁a ▁v ibr ating ▁string ▁and ▁the ▁graph ▁of ▁the ▁s ine ▁function ▁is ▁no ▁mere ▁coinc idence . ▁In ▁ocean ography , ▁the ▁res embl ance ▁between ▁the ▁shapes ▁of ▁some ▁waves ▁and ▁the ▁graph ▁of ▁the ▁s ine ▁function ▁is ▁also ▁not ▁coinc ident al . ▁In ▁some ▁other ▁fields , ▁among ▁them ▁clim at ology , ▁bi ology , ▁and ▁econom ics , ▁there ▁are ▁season al ▁periodic ities . ▁The ▁study ▁of ▁these ▁often ▁involves ▁the ▁periodic ▁nature ▁of ▁the ▁s ine ▁and ▁cos ine ▁function . ▁ ▁Fourier ▁series ▁ ▁Many ▁fields ▁make ▁use ▁of ▁trig on ometry ▁in ▁more ▁advanced ▁ways ▁than ▁can ▁be ▁discussed ▁in ▁a ▁single ▁article . ▁O ften ▁those ▁involve ▁what ▁are ▁called ▁Fourier ▁series , ▁after ▁the ▁ 1 8 th - ▁and ▁ 1 9 th - century ▁French ▁math ematic ian ▁and ▁phys ic ist ▁Joseph ▁Fourier . ▁Fourier ▁series ▁have ▁a ▁surprising ly ▁diverse ▁array ▁of ▁applications ▁in ▁many ▁scientific ▁fields , ▁in ▁particular ▁in ▁all ▁of ▁the ▁phen omena ▁involving ▁season al ▁periodic ities ▁mentioned ▁above , ▁and ▁in ▁wave ▁motion