1.诱导公式sin(-a)=-sin(a)cos(-a)=cos(a)sin(π2-兵升害生烈a)=cos(a)cos(π2-a)=sin(a来自)sin(π2+a)=cos(360问答a)cos(π2+a)=-sin(a抓金合满硫端早没)sin(π-a)=sin(a)cos(π-a)=-cos(a)sin(π+a)=-sin(a)cos(π+a)=-cos(a)2.两角和与差的三角函奏位府培数sin(a+b)=sin(a)cos(b)+cos(α)sin(b)cos(a+免短武元陆升b)=cos(a)cos(b)-sin(a)sin(b)sin(a-b)=sin(并权件照座而固特快切a)cos(b)-cos(a)零酒班拉再查sin(b)co责抗井促队s(a-b)=co杆起需过手s(a)cos(b)+sin果(a)sin(b)tan(a+b)=tan(a)+tan(b)1-tan(a)tan(b)tan(a-b)=tan(a)-tan(b)1+tan(a)tan(b)3.和差化积公式sin(a)+sin(b)=2sin(a+b2)cos(a-b2开仅府却温快雷院列)sin(a)sin(b)=2cos(a+b2)sin(a-b2)cos(a)+cos(b)=2cos(a+b2)cos(a-b2)cos(a)-cos(b)=-2sin(a+b2)sin(a-b2)4.二倍角公式sin(2a)=2sin(a)cos(b)cos(2a)=cos2(a)-sin2(a)=2cos2(a)-1=1-2sin2(a)5.半角公式sin2(a2)=1-cos(a)2cos2(a2)=1+斤专济般王齐cos(a)2tan(a2)=1-cos(a)sin(a)=sina1+cos(a)6.万校击自注东学打着能公式sin(a)兴于沉=2tan(a2)1+tan2(a2)cos(a)=1-tan2(a2)1+tan2(a2)tan(a)=2tan(a2)1-tan2(a2)7.其它公式(推导出来的)asin(a)+bcos(a)=a2+b2sin(a+c)其中tan(c)=baasin(a)+bcos(a损龙渐金旧执策克)=a2+b2co副尔威杂杂行买弦脸换s(a-c)其中tan(c)=ab1+sin(a)=(sin(a2)+cos(a2))21-sin(a)=(sin(a2)-cos(a2))2公式分类公式表达式乘法与因式分解a2-b2=(a+b)(a-b)a3+b3=(a+b)(a2-ab+b2)a3-b3=(a-b)(a2+ab+b2)三角不等式|a+b|≤|a|+|b||a-b|≤|a|+|b||a|≤b<=>-b≤a≤b|a-b|≥|a|-|b|-|a|≤a≤|a|一元二次方程的解-b+√(b2-4ac)/2a-b-b+√(b2-4ac)/2a根与系数的关系X1+X2=-b/aX1*X2=c/a注：韦达定理判别式b2-4a=0注：方程有相等的两实根b2-4ac>0注：方程有一个实根b2-4ac<0注：方程有共轭复数根三角函数公式两角和公式sin(A+B)=sinAcosB+cosAsinBsin(A-B)=sinAcosB-sinBcosAcos(A+B)=cosAcosB-sinAsinBcos(A-B)=cosAcosB+sinAsinBtan(A+B)=(tanA+tanB)/(1-tanAtanB)tan(A-B)=(tanA-tanB)/(1+tanAtanB)ctg(A+B)=(ctgActgB-1)/(ctgB+ctgA)ctg(A-B)=(ctgActgB+1)/(ctgB-ctgA)倍角公式tan2A=2tanA/(1-tan2A)ctg2A=(ctg2A-1)/2ctgacos2a=cos2a-sin2a=2cos2a-1=1-2sin2a半角公式sin(A/2)=√((1-cosA)/2)sin(A/2)=-√((1-cosA)/2)cos(A/2)=√((1+cosA)/2)cos(A/2)=-√((1+cosA)/2)tan(A/2)=√((1-cosA)/((1+cosA))tan(A/2)=-√((1-cosA)/((1+cosA))ctg(A/2)=√((1+cosA)/((1-cosA))ctg(A/2)=-√((1+cosA)/((1-cosA))和差化积2sinAcosB=sin(A+B)+sin(A-B)2cosAsinB=sin(A+B)-sin(A-B)2cosAcosB=cos(A+B)-sin(A-B)-2sinAsinB=cos(A+B)-cos(A-B)sinA+sinB=2sin((A+B)/2)cos((A-B)/2cosA+cosB=2cos((A+B)/2)sin((A-B)/2)tanA+tanB=sin(A+B)/cosAcosBtanA-tanB=sin(A-B)/cosAcosBctgA+ctgBsin(A+B)/sinAsinB-ctgA+ctgBsin(A+B)/sinAsinB
标签：Sin,cos,tan
