TEOREMAI KOSINUSHO

TEOREMAI KOSINUSHO, 1) dar trigonometriyai hamvor, teoremaest, ki bino ba on kvadrati yak tarafi sekunja ba summai kvadrathoi du tarafi digar, bo hosili zarbi duchandai in tarafho bar kosinusi kunji bayni onho barobar ast, yane

s² = a² + b²—2ab sos  (1),

ki in jo a, b, s — tarafhoi sekunja, γ — kunji bayni tarafhoi a va b; 2) dar trigonometriyai sferi, teoremaest, ki bino ba on kosinusi tarafi sekunjai sferiro ba kosinus va sinushoi du tarifi digar va kosinusi kunji bayni in tarafho ifoda mekunad:

ki in jo R — radiusi sfera. Hangomi R = 1 budan teorema mazmuni zerin dorad: kosinusi tarafi sekunjai sferi ba jami hosili zarbi kosinushoi du tarafi digar va hosili zarbi sinushoi hamon tarafhovu kosinusi kunji bayni onho barobar ast. Formulahoi

teoremai hamrohshudai teoremai kosinushoro ifoda mekunand. Hangomi R=1 budan on chunish khonda meshavad: kosinusi kunji sekunjai sferavi ba hosili zarbi sinushoi du kunji digar bar kosinusi tarafi bayni onho, be hosili zarbi kosinushoi du kunji digar barobar ast. Agar dar sekunja yake az kunjho, masalan,  kunji rost boshad:

ast va baroi R = 1, kosinusi gipotenuza ba hosili zarbi kosinushoi katetho barobar meshavad (teoremai sferavii Pifagor). Teoremai kosinushoro matematik va munajjimi suriyagi Batoni, teoremai hamrohshudaro Nasiruddini Tusi kashf kardaand.

Sh. Nuriddinov,