求一发正弦余弦正切的所有公式
发布网友
发布时间：2023-07-09 05:24
共3个回答
热心网友
时间：2024-12-02 13:11
cosα=cos(-α) cosα=-cos(π-α)=-cos(π+α) cosα=sin(π/2-α) cos2α=2cos²α-1=1-2sin²α=cos²α-sin²α cos²α=(1+cos2α)*1/2
tanα=-tan(-α) tanα=-tan(π-α)=tan(π+α) tan2α=2tanα/(1-tan²α)
sin(α±β)=sinαcosβ±cosαsinβ 符号一样 前面式子相加，后面就相加
cos(α±β)=cosαcosβ±sinαsinβ 符号相反 前面式子相减，后面就相加
tan(α+β)=(tanα+tanβ)/(1-tanαtanβ) tan(α-β)=(tanα-tanβ)/(1+tanαtanβ)追问还要还要
热心网友
时间：2024-12-02 13:11
热心网友
时间：2024-12-02 13:11
sin(2kπ+α)=sinα
cos(2kπ+α)=cosα
tan(2kπ+α)=tanα
cot(2kπ+α)=cotα
公式二:
sin(π+α)=-sinα
cos(π+α)=-cosα
tan(π+α)=tanα
cot(π+α)=cotα
公式三:
sin(-α)=-sinα
cos(-α)=cosα
tan(-α)=-tanα
cot(-α)=-cotα
公式四:
sin(π-α)=sinα
cos(π-α)=-cosα
tan(π-α)=-tanα
cot(π-α)=-cotα
公式五:
sin(2π-α)=-sinα
cos(2π-α)=cosα
tan(2π-α)=-tanα
cot(2π-α)=-cotα
公式六:
sin(π/2+α)=cosα
cos(π/2+α)=-sinα
tan(π/2+α)=-cotα
cot(π/2+α)=-tanα
sin(π/2-α)=cosα
cos(π/2-α)=sinα
tan(π/2-α)=cotα
cot(π/2-α)=tanα追问再来点
追答tgA=tanA=sinAcosA
1.两角和与差
sin(a+b)=sin(a)cos(b)+cos(α)sin(b)
cos(a+b)=cos(a)cos(b)-sin(a)sin(b)
sin(a-b)=sin(a)cos(b)-cos(a)sin(b)
cos(a-b)=cos(a)cos(b)+sin(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)
2.和差化积公
sin(a)+sin(b)=2sin(a+b2)cos(a-b2)
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)
3.积化和差 (上面的反过来)
sin(a)sin(b)=-12⋅[cos(a+b)-cos(a-b)]
cos(a)cos(b)=12⋅[cos(a+b)+cos(a-b)]
sin(a)cos(b)=12⋅[sin(a+b)+sin(a-b)]
4.二倍角公式
sin(2a)=2sin(a)cos(a)
cos(2a)=cos2(a)-sin2(a)=2cos2(a)-1=1-2sin2(a)
5.半角公式
sin2(a2)=1-cos(a)2
cos2(a2)=1+cos(a)2
tan(a2)=1-cos(a)sin(a)=sina1+cos(a)
6.其他
sin(a)=2tan(a2)1+tan2(a2)
cos(a)=1-tan2(a2)1+tan2(a2)
tan(a)=2tan(a2)1-tan2(a2)
a⋅sin(a)+b⋅cos(a)=a2+b2sin(a+c) 其中 tan(c)=ba
a⋅sin(a)-b⋅cos(a)=a2+b2cos(a-c) 其中 tan(c)=ab
1+sin(a)=(sin(a2)+cos(a2))2
1-sin(a)=(sin(a2)-cos(a2))2
csc(a)=1sin(a)
sec(a)=1cos(a)
差不多就这些了吧
