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Trigonometrijske formule

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Trigonometrijske formule

  1. 1. Trigonometrijske formule<br /><ul><li>4276725221615π=180o00π=180oOsnovne formule</li></ul>4276725376555k∈Z00k∈Zsin2x+cos2x=1<br />tgx=sinxcosx; x≠π2+πk<br />ctgx=cosxsinx; x≠πk<br />tgx=1ctgx<br />sin360ok+x=sinx<br />cos360ok+x=cosx<br />tg180ok+x=tgx<br />ctg180ok+x=ctgx<br />sin-x=-sinx<br />cos-x=cosx<br />tg-x=-tgx<br />ctg-x=-ctgx<br /><ul><li>Adicione formule</li></ul>sinx±y=sinxcosy±cosxsiny<br />cosx±y=cosxcosy∓sinxsiny<br />tg(x±y)=tgx±tgy1∓tgxtgy<br />ctgx±y=1∓tgxtgytgx±tgy<br /><ul><li>Formule dvostrukog ugla</li></ul>sin2x=2sinxcosx<br />cos2x=cos2x-sin2x<br />tg2x=2tgx1-tg2x<br /><ul><li>Formule poluugla</li></ul>|sinx2|=1-cosx2<br />|cosx2|=1+cosx2<br />|tgx2|=1-cosx1+cosx<br /><ul><li>Formule trostrukog ugla</li></ul>sin3x=3sinx-4sin3x<br />cos3x=4cos3x-3cosx<br /><ul><li>Transformacija proizvoda trigonometrijskih fukncija u zbir ili razliku</li></ul>sinxsiny=12(cosx-b-cosx+y)<br />sinxcosy=12(sinx-b+sinx+y)<br />cosxcosy=12(cosx-b+cosx+y)<br /><ul><li>Transformacija zbira i razlike trigonometrijskih fukncija u proizvod</li></ul>sinx+siny=2sinx+y2cosx-y2<br />sinx-siny=2cosx+y2sinx-y2<br />cosx+cosy=2cosx+y2cosx-y2<br />cosx-cosy=-2sinx+y2sinx-y2<br />tgx±tgy=sin(x±y)cosxcosy<br />ctgx±ctgy=sin(y±x)sinxsiny<br /><ul><li>Vrednosti trigonometrijskih funkcija uglova</li></ul>561975721360sin60o=32cos60o=12tg60o=3ctg60o=33020000sin60o=32cos60o=12tg60o=3ctg60o=332019300721360sin30o=12cos30o=32tg30o=33ctg30o=3020000sin30o=12cos30o=32tg30o=33ctg30o=33476625721360sin45o=22cos45o=22tg45o=1ctg45o=1020000sin45o=22cos45o=22tg45o=1ctg45o=1<br /><ul><li>Svođenje na prvi kvadrant</li></ul>xπ2-xπ2+xπ-xπ+x3π2-x3π2+x2π-x2π+xsinxcosxcosxsinx-sinx-cosx-cosx-sinxsinxcosxsinx-sinx-cosx-cosx-sinxsinxcosxcosxtgxctgx-ctgx-tgxtgxctgx-ctgx-tgxtgxctgxtgx-tgx-ctgxctgxtgx-tgx-ctgxctgx<br />

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