三角函数MicrosoftWord文档.doc

sin =/ cos =/tan =/cot =/sin2A=2sinA?cosAcos2A=cos2A-sin2A=1-2sin2A=2cos2A-1tan2A=2tanA/1-tan2Asin3=4sinsin(/3+)sin(/3-)cos3=4coscos(/3+)cos(/3-)tan3a = tan a tan(/3+a) tan(/3-a)1sin3a=sin(2a+a)=sin2acosa+cos2asina=2sina(1-sin2a)+(1-2sin2a)sina=3sina-4sin3a2.cos3a=cos(2a+a)=cos2acosa-sin2asina=(2cos2a-1)cosa-2(1-cosa)cosa=4cos3a-3cosa3 sin3a=3sina-4sin3a=4sina(3/4-sin2a)=4sina(3/2)2-sin2a=4sina(sin260-sin2a)=4sina(sin60+sina)(sin60-sina)=4sina*2sin(60+a)/2cos(60-a)/2*2sin(60-a)/2cos(60-a)/2=4sinasin(60+a)sin(60-a)4 cos3a=4cos3a-3cosa=4cosa(cos2a-3/4)=4cosacos2a-(3/2)2=4cosa(cos2a-cos230)=4cosa(cosa+cos30)(cosa-cos30)=4cosa*2cos(a+30)/2cos(a-30)/2*-2sin(a+30)/2sin(a-30)/2=-4cosasin(a+30)sin(a-30)=-4cosasin90-(60-a)sin-90+(60+a)=-4cosacos(60-a)-cos(60+a)=4cosacos(60-a)cos(60+a)5 tan3a=tanatan(60-a)tan(60+a)tan(A/2)=(1-cosA)/sinA=sinA/(1+cosA);cot(A/2)=sinA/(1-cosA)=(1+cosA)/sinA.sin2(a/2)=(1-cos(a)/2cos2(a/2)=(1+cos(a)/2tan(a/2)=(1-cos(a)/sin(a)=sin(a)/(1+cos(a)?sin+sin = 2 sin(+)/2 cos(-)/2?sin-sin = 2 cos(+)/2 sin(-)/2cos+cos = 2 cos(+)/2 cos(-)/2cos-cos = -2 sin(+)/2 sin(-)/2tanA+tanB=sin(A+B)/cosAcosB=tan(A+B)(1-tanAtanB)tanA-tanB=sin(A-B)/cosAcosB=tan(A-B)(1+tanAtanB)sinsin = cos(-)-cos(+) /2coscos = cos(+)+cos(-)/2sincos = sin(+)+sin(-)/2cossin = sin(+)-sin(-)/2sinh(a) = ea-e(-a)/2cosh(a) = ea+e(-a)/2tanh(a) = sin h(a)/cos h(a)sin2k= sincos2k= costan2k= tancot2k= cot+sin= -sincos= -costan= tancot= cot -sin-= -sincos-= costan-= -tancot-= -cot-sin-= sincos-= -costan-= -tancot-= -cot-2-sin2-= -sincos2-= costan2-= -tancot2-= -cot/23/2sin/2+= coscos/2+= -sintan/2+= -cotcot/2+= -tansin/2-= coscos/2-= sintan/2-= cotcot/2-= tansin3/2+= -coscos3/2+= sintan3/2+= -cotcot3/2+= -tansin3/2-= -coscos3/2-= -sintan3/2-= cotcot3/2-= tan(kZ)Asin(t+)+ Bsin(t+) =(A2 +B2 +2ABcos(-) ? sin t + arcsin (A?sin+B?sin) / A2 +B2; +2ABcos(-) ,sin(-) = -sincos(-) = costan (-)=-tansin(/2-) = coscos(/2-) = sinsin(/2+) = coscos(/2+) = -sinsin(-) = sincos(-) = -cossin(+) = -sincos(+) = -costanA= sinA/cosAtan/2cottan/2cottantantantan (sin)2+(cos)2=1(2)1+(tan)2=(sec)2(3)1+(cot)2=(csc)2,(sin)2,(cos)2(4),tanA+tanB+tanC=tanAtanBtanC:A+B=-Ctan(A+B)=tan(-C)(tanA+tanB)/(1-tanAtanB)=(tan-tanC)/(1+tantanC)tanA+tanB+tanC=tanAtanBtanC,x+y+z=n(nZ),tanA+tanB+tanC=tanAtanBtanC(5)cotAcotB+cotAcotC+cotBcotC=1(6)cot(A/2)+cot(B/2)+cot(C/2)=cot(A/2)cot(B/2)cot(C/2)(7)(cosA2+(cosB2+(cosC2=1-2cosAcosBcosC(8)sinA2+sinB2+sinC2=2+2cosAcosBcosCcsc(a) = 1/sin(a)sec(a) = 1/cos(a) sin22sincoscos2cos2sin22cos2112sin22tantan21tan2sin33sin4sin3cos34cos33cos3tantan3tan313tan2 sinsin2sincos2 2 sinsin2cossin2 2 coscos2coscos2 2 coscos2sinsin2 2 1sin cos-sinsin21cos sin-sinsin21cos cos-coscos21sin sin -coscos2asin bcos/tools/maths/.1?1sin=y/ r; cos=x/r; tan=y/x; cot=x/ysin(A+B) = sinAcosB+cosAsinB XCDABAODBODAOBOBODAODA(cos,sin),B(cos,sin),A(cos(-),sin(-)OA=OA=OB=OD=1,D(1,0)cos(-)-12+sin(-)2=(cos-cos)2+(sin-sin)2(a+b)/2(a-b)/2 0 /2 x x y cos sin 1 sin = y/1 cos = x/1 1?sin(A+B) = sinAcosB+cosAsinBsin(A-B) = sinAcosB-cosAsinBcos(A+B) = cosAcosB-sinAsinBcos(A-B