▁manufact ur ers ▁of ▁the ▁United ▁States <0x0A> </s> ▁Among st ▁the ▁lay ▁public ▁of ▁non - math emat icians ▁and ▁non - s cient ists , ▁trig on ometry ▁is ▁known ▁chief ly ▁for ▁its ▁application ▁to ▁measurement ▁problems , ▁yet ▁is ▁also ▁often ▁used ▁in ▁ways ▁that ▁are ▁far ▁more ▁subt le , ▁such ▁as ▁its ▁place ▁in ▁the ▁theory ▁of ▁music ; ▁still ▁other ▁uses ▁are ▁more ▁technical , ▁such ▁as ▁in ▁number ▁theory . ▁The ▁mathematical ▁topics ▁of ▁Fourier ▁series ▁and ▁Fourier ▁transform s ▁rely ▁heavily ▁on ▁knowledge ▁of ▁trig on ometric ▁functions ▁and ▁find ▁application ▁in ▁a ▁number ▁of ▁areas , ▁including ▁statistics . ▁ ▁Thomas ▁Pa ine ' s ▁statement ▁ ▁In ▁Chapter ▁XI ▁of ▁The ▁Age ▁of ▁Re ason , ▁the ▁American ▁revolution ary ▁and ▁En light en ment ▁think er ▁Thomas ▁Pa ine ▁wrote : ▁▁ ▁The ▁scientific ▁principles ▁that ▁man ▁emp lo ys ▁to ▁obtain ▁the ▁for ek now ledge ▁of ▁an ▁eclipse , ▁or ▁of ▁any ▁thing ▁else ▁rel ating ▁to ▁the ▁motion ▁of ▁the ▁heaven ly ▁bodies , ▁are ▁contained ▁chief ly ▁in ▁that ▁part ▁of ▁science ▁that ▁is ▁called ▁trig on ometry , ▁or ▁the ▁properties ▁of ▁a ▁triangle , ▁which , ▁when ▁applied ▁to ▁the ▁study ▁of ▁the ▁heaven ly ▁bodies , ▁is ▁called ▁astronom y ; ▁when ▁applied ▁to ▁direct ▁the ▁course ▁of ▁a ▁ship ▁on ▁the ▁ocean , ▁it ▁is ▁called ▁navigation ; ▁when ▁applied ▁to ▁the ▁construction ▁of ▁figures ▁drawn ▁by ▁a ▁r uler ▁and ▁comp ass