各種三角函數(shù)關(guān)系式

1、tanacota=1sinacsca=1cosaseca=1sin2a+cos2a=11+tan2a=sec2a1+cot2a=csc2asina/cosa=tana=seca/cscacosa/sina=cota=csca/secasin(a)=sinacos(a)cosasin(n/2a)=cosasin(na)=sinacos(n/2a)=sinacos(na)=cosatan(n/2a)=cotatan(na)=tanacot(n/2a)=tanacot(na)=cotasin(n/2+a)=cosasin(n+a)=sinacos(n/2+a)=sinacos(n+a)=cosata

2、n(n/2+a)=cotatan(n+a)=tanacot(n/2+a)=tanacot(n+a)=cota兩角和與差的三角函數(shù)公式sin(a+B)=sinacosg+cosasinBsin(ag)=sinacosgcosasingcos(a+g)=cosacosgsinasingcos(aB)=cosacosg+sinasingtana+tangtan(a+g)=1tanatangtanatang誘導(dǎo)公式tan(a)=tanacot(a)=cotasin(3n/2a)=cosasin(2na)=sinacos(3n/2a)=sinacos(2na)=cosatan(3n/2a)=cotata

3、n(2na)=tanacot(3n/2a)=tanacot(2na)=cotasin(3n/2+a)=cosasin(2kn+a)=sinacos(3n/2+a)=sinacos(2kn+a)=cosatan(3n/2+a)=cotatan(2kn+a)=tanacot(3n/2+a)=tanacot(2kn+a)=cota(其中kwZ)萬能公式2tan(a/2)sina=1+tan2(a/2)1tan2(a/2)cosa=1+tan2(a/2)2tan(a/2)tana=tan(aB)=1+tanatanB半角的正弦、余弦和正切公式1tan2（a/2）三角函數(shù)的降幕公式1-c：osa_sin

4、cesince1+:cosa二倍角的正弦、余弦和正切公式sin2a=2sinacosacos2a=cos2asin2a=2cos2a1=12sin2a2tanatan2a=1tan2a三倍角的正弦、余弦和正切公式sin3a=3sina4sin3acos3a=4cos3a3cosa3tanatan3atan3a=13tan2a三角函數(shù)的積化和差公式三角函數(shù)的和差化積公式sina+sinp=2sincos22a+papsina-cosp=-sin(a+p)+sin(ap)cosa-sinp=-sin(a+p)sin(ap)cosa-cosp=-cos(a+p)+cos(ap)sina-sinp=-cos(a+p)cos(ap)sinasinp=2cossin22a+papcosa+cosp=2coscos22a+papc