三角函数公式汇总

总律律三角函数的本质及内部规律就会发现三角函数内部规律及本质也是学好三角函数的关键所在.sinθ=y/R;cosθ=x/R;tanθ=y/x;cotθ=x/y。可以从这里出发推导出来，比如以推导sin(A+B)=sinAcosB+cosAsinB为例：tan(A-B)=(tanA-tanB)/(1+tanAtanB)cot(A+B)=(cotAcotB-1)/(cotB+cotA)cot(A-B)=(cotAcotB+1)/(cotB-cotA)倍角公式AosASinASinACosA^2-1)三倍角公式tan3a=tana·tan(π/3+a)·tan(π/3-a)半角公式tanA(1-cosA)/sinA=sinA/(1+cosA);cotAsinAcosAcosAsinA和差化积sin(a)+sin(b)=2sin[(a+b)/2]cos[(a-b)/2]sin(a)-sin(b)=2cos[(a+b)/2]sin[(a-b)/2]cos(a)+cos(b)=2cos[(a+b)/2]cos[(a-b)2]cos(a)-cos(b)=-2sin[(a+b)/2]sin[(a-b)/AtanBsinABcosAcosB积化和差sin(a)sin(b)=-1/2*[cos(a+b)-cos(a-b)]cos(a)cos(b)=1/2*[cos(a+b)+cos(a-b)]sin(a)cos(b)=1/2*[sin(a+b)+sin(a-b)]cos(a)sin(b)=1/2*[sin(a+b)-sin(a-b)]诱导公式sin(-a)=-sin(a)cos(-a)=cos(a)sin(π/2-a)=cos(a)cos(π/2-a)=sin(a)sin(π/2+a)=cos(a)cos(π/2+a)=-sin(a)sin(π-a)=sin(a)cos(π-a)=-cos(a)sin(π+a)=-sin(a)cos(π+a)=-cos(a)tanA=sinA/cosAtan(π/2＋α)＝－cotαtan(π/2－α)＝cotαtan(π－α)＝－tanαtan(π＋α)＝tanα公式其它公式证明下面两式,只需将一式,左右同除(sinα)(cosα)^2即可对于任意非直角三角形,总有tanBtanCtanAtanBtanCA+B=π-CtanAB)=tan(π-C)nBtanAtanBtantanCtanBtanCtanAtanBtanC其他非重点三角函数==双曲函数sinh(a)=[e^a-e^(-a)]/2cosh(a)=[e^a+e^(-a)]/2tgh(a)=sinh(a)/cosh(a)sin(2kπ＋α)=sinαcos(2kπ＋α)=cosαtan(kπ＋α)=tanαcot(kπ＋α)=cotαsin(π＋α)=-sinαcos(π＋α)=-cosαtan(π＋α)=tanαcot(π＋α)=cotαsin(-α)=-sinαcos(-α)=cosαtan(-α)=-tanαcot(-α)=-cotαsin(π-α)=sinαcos(π-α)=-cosαtan(π-α)=-tanαcot(π-α)=-cotαsin(2π-α)=-sinαcos(2π-α)=cosαtan(2π-α)=-tanαcot(2π-α)=-cotαsin(π/2+α)=cosαcos(π/2+α)=-sinαtan(π/2+α)=-cotαcot(π/2+α)=-tanαsin(π/2-α)=cosαcos(π/2-α)=sinαtan(π/2-α)=cotαcot(π/2-α)=tanαsin(3π/2+α)=-cosαcos(3π/2+α)=sinαtan(3π/2+α)=-cotαcot(3π/2+α)=-tanαsin(3π/2-α)=-cosαcos(3π/2-α)=-sinαtan(3π/2-α)=cotαcot(3π/2-α)=tanα这个物理常用公式我