TRIGONOMETRIYa

TRIGONOMETRIYa (az yunoni trigonon — sekunja va ..metriya), yak fasli matematikaro guyand, ki funksiyahoi trigonometri va tatbiqi onhoro dar geometriya meomuzad. Trigonometriya hamvor yo rostkhatta va sferavi meshavad. Nazariyai funksiyahoi trigonometri (goniometriya) va tatbiqi on dar halli sekunjahoi hamvori rostkunja va kajkunja predmeti talimi maktabi miyona meboshad.

Formulahoi asosii trigonometriyai hamvor. Biguzor a, b, s — tarafhoi sekunja, A, V, S kunjhoi muqobili in tarafho (A + V + S = ), h_a, h_b, h_s — balandihoi ba in tarafho farovardashuda, 2r — perimetr, S — masohat va 2R — diametri davrai beruntasviri sekunja boshand, pas formulahoi zerin joy dorand: teoremai sinusho:

= ==2R,

teoremai kosinusho:

a² = b² + s² — 2 b · s sos A, teoremai tangensho:

=

masohati sekunja:

S= ab sin C= · = p² tg  · tg  · tg  .

Agar tarafhoi sekunja malum boshand, kunjhoi onro ap rui teoremai kosiyusho yo formulai:

Tg =  =  yoftan mumkin ast.

Trigonometriyai hamvor bad az trigonometriyai  sferavi inkishof yoftaast. (Harchand, ki teoremahoi alohidai on peshtar malum budand). Masalan, teoremahoi 12 va 13-umi kitobi duyumi «Usuli» Uqlidus (teoremai kosinushoro ifoda mekunad. Trigonometriyai hamvorro Battoni, Abulvafoi Buzajoni, Bhaskara (asri 12) va Nasiruddini Tusi, ki bo teoremai sinusho shinos budand, inkishof dodaand. Teoremai tangenshoro Regiomontan (asri 15) isbot namudaast. N. Kopernik, T. Vrage, F. Viet, I. Kepler dar inkishofi Trigonometriya sahmi kalon guzoshtaand. L. Eyler Trigonometriyairo dar namudi hozira murattab kardaast.