cos²α+sin²α=1cosα=1/兄派基secαsinα=1/cscαtanα=1/cotα1/sec²α+1/csc²α=11+tan²α=sec²α=1/cos²α1+cot²α=csc²α=1/sin²αcos(α+β)=cosαcosβ-sinαsinβ cos(α-β)=cosαcosβ+sinαsinβsin(α+β)=sinαcosβ+cosαsinβsin(α-β)=sinαcosβ-cosαsinβtan(α+β)=(tanα+tanβ)/(1-tanαtanβ)tan(α-β)=(tanα-tanβ)/(1+tanαtanβ)二倍角sin2α=2sinαcosα 1+2sin2α=(sinα+cosα)² cos2α=cos²α-sin²α=1-2sin²α=2cos²-1tan2α=2tanα/(1+tan²α)半角sin²(α/2)=(1-cosα)/2cos²(α/2)=(1+cosα)/2tan²(α/2)=(1-cosα)/(1+cos)tan(α/2)=(1-cosα)/sinα=sinα/(1+cosα)万能置换公式sinα=2tan(α/2)/[1+tan(α/羡销2)]cosα=[1+tan(α/2)]/[1-tan(α/2)]tanα=2tan(α/2)/[1-tan(α/2)]和差化积公式sin α+sinβ=2sin[(α+β)/2]·cos[(α-β)/2]sin α-sin β=2cos[(α+β)/2]·sin[(α-β)/2]cos α+cos β=2cos[(α+β)/2]·cos[(α-β)/2]cos α-cos β=-2sin[(α+β)/2]·sin[(α-β)/2]积化和差公式sinαsinβ=-[cos(α+β)-cos(α-β)]/2cosαcosβ=[cos(α+β)+cos(α-β)]/2sinαcosβ=[sin(α+β)+sin(α-β)]/2cosαsinβ=[sin(α+β)-sin(α-β)]/2以下是诱导公式公式一：sin(2kπ+α)=sinα (k∈Z)cos(2kπ+α)=cosα (k∈Z)tan(2kπ+α)=tanα (k∈Z)cot(2kπ+α)=cotα (k∈Z)sec(2kπ+α)=secα (k∈Z)csc(2kπ+α)=cscα (k∈Z)公式二：sin(π+α)=-sinαcos(π+α)=-cosαtan(π+α)=tanαcot(π+α)=cotαsec(π+α)=-secαcsc(π+α)=-cscα公式三：sin(-α)=-sinαcos(-α)=cosαtan(-α)=-tanαcot(-α)=-cotαsec(-α)=secαcsc(-α)=-cscα公式四：sin(π-α)=sinαcos(π-α)=-cosαtan(π-α)=-tanαcot(π-α)=-cotαsec(π-α)=-secαcsc(π-α)=cscα公式五：sin(2π-α)=-sinαcos(2π-α)=cosαtan(2π-α)=-tanαcot(2π-α)=-cotαsec(2π-α)=secαcsc(2π-α)=-cscα公式六羡谨：1、sin(π/2+α)=cosαcos(π/2+α)=-sinαtan(π/2+α)=-cotαcot(π/2+α)=-tanαsec(π/2+α)=-cscαcsc(π/2+α)=secα2、sin(π/2-α)=cosαcos(π/2-α)=sinαtan(π/2-α)=cotαcot(π/2-α)=tanαsec(π/2-α)=cscαcsc(π/2-α)=secα3、sin(3π/2+α)=-cosαcos(3π/2+α)=sinαtan(3π/2+α)=-cotαcot(3π/2+α)=-tanαsec(3π/2+α)=cscαcsc(3π/2+α)=-secα4、sin(3π/2-α)=-cosαcos(3π/2-α)=-sinαtan(3π/2-α)=cotαcot(3π/2-α)=tanαsec(3π/2-α)=-cscαcsc(3π/2-α)=-secα
标签：三角函数,公式
