Funkcje trygonometryczne (wzory)
ZALEŻNOŚCI sin(a+b)=sinacosb+cosasinb sin(a-b)=sinacosb-cosasinb sin(2a)=2sinacosa sin(3a)=sina(3-4sin2a) cos(a+b)=cosacosb-sinasinb cos(a-b)=cosacosb+sinasinb cos(2a)=cos2a-sin2a=1-2sin2a=2cos2a-1 cos(3a)=(4cos2a-3)cosa tg(a+b)=(tga+tgb)/(1-tgatgb) tg(a-b)=(tga-tgb)/(1+tgatgb) tg2a=2tga/(1-tg2a) tg3a=tga(3-tg2a)/(1-3tg2a) ctg(a+b)=(ctgactgb-1)/(ctga+ctgb) ctg(a-b)=(ctgactgb+1)/(ctgb-ctga) ctg2a=(ctg2a-1)/2ctga ctg3a=ctga(ctg2a-3)/(3ctg2a-1)
sina+sinb=2sin((a+b)/2)cos((a-b)/2) sina-sinb=2cos((a+b)/2)sin((a-b)/2) cosa+cosb=2cos((a+b)/2)cos((a-b)/2) cosa-cosb=-2sin((a+b)/2)sin((a-b)/2) tga-tgb=sin(a-b)/cosacosb ctga-ctgb=-sin(a-b)/sinasinb sin2a-sin2b=cos2b-cos2a=sin(a+b)sin(a-b)
sina=tga/Ö(1+tg2a) sin2a=(1-cos2a)/2 cosa=1/Ö(1+tg2a) cos2a=(1+cos2a)/2 sin2a=2tga/(1+tg2a) cos2a=(1-tg2a)/(1+tg2a) tg2a=(1-cos2a)/(1+cos2a)=sin22a/(1+cos2a)2=(1-cos2a)2/sin22a
WZORY REDUKCYJNEsin(-x)=sin(180°+x)=cos(90°+x)=cos(270°-x)=-sin(x) cos(-x)=sin(90°-x)=sin(90°+x)=cos(x) sin(180°-x)=cos(90°-x)=cos(270°+x)=sin(x) cos(180°-x)=cos(180°+x)=sin(270°-x)=sin(270°+x)=-cos(x) tg(-x)=tg(180°-x)=ctg(90°+x)=ctg(270°+x)=-tg(x) ctg(-x)=ctg(180°-x)=tg(90°+x)=tg(270°+x)=-ctg(x) tg(180°+x)=ctg(90°-x)=ctg(270°-x)=tg(x) ctg(180°+x)=tg(90°-x)=tg(270°-x)=ctg(x)
WARTOŚCI FUNKCJIsin(0°)=0, sin(30°)=1/2, sin(45°)=Ö2/2, sin(60°)=Ö3/2, sin(90°)=1 cos(0°)=1, cos(30°)=Ö3/2, cos(45°)=Ö2/2, cos(60°)=1/2, cos(90°)=0 tg(0°)=0, tg(30°)=Ö3/3, tg(45°)=1, tg(60°)=Ö3, tg(90°)ÎĆ ctg(0°)ÎĆ, ctg(30°)=Ö3, ctg(45°)=1, ctg(60°)=Ö3/3, ctg(90°)=0, sin15°=cos75°=Ö(2-Ö3)/2 cos15°=sin75°=Ö(2+Ö3)/2 tg15°=ctg75°=2-Ö3 ctg15°=ctg75°=2+Ö3 sin(22,5°)=cos(67,5°)=Ö(2-Ö2)/2 cos(22,5°)=sin(67,5°)=Ö(2+Ö2)/2 tg(22,5°)=ctg(67,5°)=Ö2-1 ctg(22,5°)=tg(67,5°)=Ö2+1
Kony777