▁products ▁of ▁trig on ometric ▁functions ▁of ▁those ▁angles . ▁ ▁Some ▁modern ▁uses ▁ ▁Scient ific ▁fields ▁that ▁make ▁use ▁of ▁trig on ometry ▁include : ▁ ▁ac oust ics , ▁architecture , ▁astronom y , ▁cart ography , ▁civil ▁engineering , ▁ge oph ys ics , ▁cry stal log raph y , ▁elect rical ▁engineering , ▁electron ics , ▁land ▁surve ying ▁and ▁ge odes y , ▁many ▁physical ▁sciences , ▁mechanical ▁engineering , ▁mach ining , ▁medical ▁imag ing , ▁number ▁theory , ▁ocean ography , ▁opt ics , ▁ph arm ac ology , ▁probability ▁theory , ▁se ism ology , ▁statistics , ▁and ▁visual ▁per ception ▁ ▁That ▁these ▁fields ▁involve ▁trig on ometry ▁does ▁not ▁mean ▁knowledge ▁of ▁trig on ometry ▁is ▁needed ▁in ▁order ▁to ▁learn ▁anything ▁about ▁them . ▁It ▁does ▁mean ▁that ▁some ▁things ▁in ▁these ▁fields ▁cannot ▁be ▁understood ▁without ▁trig on ometry . ▁For ▁example , ▁a ▁professor ▁of ▁music ▁may ▁perhaps ▁know ▁nothing ▁of ▁mathematics , ▁but ▁would ▁probably ▁know ▁that ▁P yth ag or as ▁was ▁the ▁earliest ▁known ▁contrib utor ▁to ▁the ▁mathematical ▁theory ▁of ▁music . ▁ ▁In ▁some ▁of ▁the ▁fields ▁of ▁ende avor ▁listed ▁above ▁it ▁is ▁easy ▁to ▁imagine ▁how ▁trig on ometry ▁could ▁be ▁used . ▁For ▁example , ▁in ▁navigation ▁and ▁land ▁surve ying , ▁the ▁occasions ▁for ▁the ▁use ▁of ▁trig on ometry ▁are ▁in ▁at ▁least ▁some ▁cases ▁simple ▁enough ▁that ▁they ▁can ▁be ▁described ▁in ▁a ▁beginning ▁trig on ometry ▁text