Òðèãîíîìåòðèÿ àëãåáðà ARCSIN a -p/2£arcsin a £p/2 sin(arcsin a)=a arcsin (-a)= -arcsin a a 0 1/2 Ö2/2 Ö3/2 1 arcsin a 0 p/6 p/4 p/3 p/2 SIN X= A x=(-1)n arcsin a +pk sin x=0 x=pk sin x=1 x=p/2+2pk sin x=-1 x=-p/2+2pk ARCCOS a 0 £arccos a £p cos(arccos a)=a arccos (-a)=p -arccos a a 0 1/2 Ö2/2 Ö3/2 1 arccos a p/2 p/3 p/4 p/6 0 COS X= A x=± arccos a +2pk cos x=0 x=p/2+pk cos x=1 x=2pk cos x=-1 x=p+2pk ARCTG a -p/2£arctg a £p/2 tg(arctg a)=a arctg (-a)= -arctg a a 0 Ö3/3 1 Ö3 tg a 0 p/6 p/4 p/3 TG X= A x=± arctg a +pk sina*cosb=1/2[sin(a-b)+sin(a+b)] sina*sinb=1/2[cos(a-b)-cos(a+b)] cosa*cosb=1/2[cos(a-b)+cos(a+b)] sina*cosb=1/2[sin(a-b)+sin(a+b)] sina*sinb=1/2[cos(a-b)-cos(a+b)] cosa*cosb=1/2[cos(a-b)+cos(a+b)] sina+sinb=2sin(a+b)/2 * cos(a-b)/2 sina-sinb=2sin(a-b)/2 * cos(a+b)/2 cosa+cosb=2cos(a+b)/2 * cos(a-b)/2 cosa-cosb=-2sin(a+b)/2 * sin(a-b)/2 (a+b)2=a2+2ab+b2 (a-b)2=a2+2ab+b2 (a+b+c)2=a2+b2+c2+2ab+2ac+2bc a2-b2=(a-b)(a+b) (a+b)3=a3+3a2b+3ab2+b3 (a-b)3=a3-3a2b+3ab2-b3 a3+b3=(a+b)(a2-ab+b2) a3-b3=(a-b)(a2+ab+ b2) 0 p/6 p/4 p/3 p/2 p 2/3p 3/4p 5/6p 3/2p 0 30° 45° 60° 90° 180 120° 135° 150° 270° sin 0 1/2 Ö2/2 Ö3/2 1 0 Ö3/2 Ö2/2 1/2 -1 cos 1 Ö3/2 Ö2/2 1/2 0 -1 -1/2 -Ö2/2 -Ö3/2 0 tg 0 1/Ö3 1 Ö3 - 0 -Ö3 -1 -1/Ö3 - ctg - Ö3 1 1/Ö3 0 - -1/Ö3 -1 -Ö3 0 sin2+cos2=1 sin=±Ö1-cos2 sin(-a)=-sina tg(-a)=-tga tg•ctg=1 cos=±Ö1-sin2 cos(-a)=cosa ctg(-g)=-ctga tg=1/ctg ctg=1/tg 1+tg2=1/cos2=sec2 sin2=(1-cos)(1+cos) 1+ctg2=1/sin2=cosec2 sin2a=2sina•cosa cos2=(1-sin)(1+sin) 1-tg2/(1+tg2)=cos4-sin4 cos2a=cos2 a-sin2 a cos/(1-sin)=1+sin/cos 1/(tg+ctg)=sin•cos tg2a=2tga/1-tga cos(a+b)=cosa•cosb-sina•sinb sin3a=3sina-4sin3a cos(a-b)=cosa•cosb+sina•sinb cos3a=4cos3a-3cosa sin(a+b)=sina•cosb+cosa•sinb tg(a+b)=tga+tgb sin(a-b)=sina•cosb-cosa•sinb 1-tga•tgb 2cos2a/2=1+cosa 2sin2a/2=1-cosa 0 p/6 p/4 p/3 p/2 p 2/3p 3/4p 5/6p 3/2p 0 30° 45° 60° 90° 180 120° 135° 150° 270° sin 0 1/2 Ö2/2 Ö3/2 1 0 Ö3/2 Ö2/2 1/2 -1 cos 1 Ö3/2 Ö2/2 1/2 0 -1 -1/2 -Ö2/2 -Ö3/2 0 tg 0 1/Ö3 1 Ö3 - 0 -Ö3 -1 -1/Ö3 - ctg - Ö3 1 1/Ö3 0 - -1/Ö3 -1 -Ö3