锟竭讹拷锟斤拷(sh锟斤拷)锟絎锟斤拷锟斤拷锟角猴拷锟斤拷(sh锟斤拷)知锟絉锟絚

2024-09-11 11:25:23锟絎(w锟斤拷ng)锟絡(lu锟斤拷)锟斤拷锟斤拷

锟斤拷锟斤拷锟絁锟斤拷锟斤拷锟角猴拷锟斤拷(sh锟斤拷)锟斤拷锟絰

锟斤拷锟斤拷锟絁锟角斤拷A锟斤拷锟斤拷锟斤拷(sin),锟斤拷锟斤拷(cos)锟斤拷锟斤拷锟斤拷(tan),锟斤拷锟斤拷(cot)锟皆硷拷锟斤拷锟斤拷(sec)锟斤拷锟斤拷锟�(csc)锟斤拷锟斤拷锟斤拷锟斤拷A锟斤拷锟絁锟斤拷锟斤拷锟角猴拷锟斤拷(sh锟斤拷)锟斤拷

锟斤拷锟斤拷锟斤拷锟斤拷(sin)锟斤拷锟节岋拷邊锟斤拷斜邊;sinA=a/c

锟斤拷锟斤拷锟斤拷锟斤拷(cos)锟斤拷锟斤拷锟斤拷邊锟斤拷斜邊;cosA=b/c

锟斤拷锟斤拷锟斤拷锟斤拷(tan)锟斤拷锟节岋拷邊锟斤拷锟斤拷邊;tanA=a/b

锟斤拷锟斤拷锟斤拷锟斤拷(cot)锟斤拷锟斤拷锟斤拷邊锟饺岋拷邊;cotA=b/a

锟斤拷锟斤拷锟斤拷锟斤拷(sec)锟斤拷锟斤拷斜邊锟斤拷锟斤拷邊;secA=c/b

锟斤拷锟斤拷锟斤拷锟�(csc)锟斤拷锟斤拷斜邊锟饺岋拷邊锟斤拷cscA=c/a

锟斤拷锟斤拷锟斤拷锟斤拷堑锟斤拷锟斤拷呛锟斤拷锟�(sh锟斤拷)锟絞锟斤拷锟絇(gu锟斤拷n)系

锟斤拷锟斤拷sin(90°-α)=cosα, cos(90°-α)=sinα,

锟斤拷锟斤拷tan(90°-α)=cotα, cot(90°-α)=tanα.

锟斤拷锟斤拷平锟斤拷锟絇(gu锟斤拷n)系锟斤拷

锟斤拷锟斤拷sin^2(α)+cos^2(α)=1

锟斤拷锟斤拷tan^2(α)+1=sec^2(α)

锟斤拷锟斤拷cot^2(α)+1=csc^2(α)

锟斤拷锟斤拷锟絜锟斤拷锟絇(gu锟斤拷n)系锟斤拷

锟斤拷锟斤拷sinα=tanα·cosα

锟斤拷锟斤拷cosα=cotα·sinα

锟斤拷锟斤拷tanα=sinα·secα

锟斤拷锟斤拷cotα=cosα·cscα

锟斤拷锟斤拷secα=tanα·cscα

锟斤拷锟斤拷cscα=secα·cotα

锟斤拷锟斤拷锟斤拷锟斤拷(sh锟斤拷)锟絇(gu锟斤拷n)系锟斤拷

锟斤拷锟斤拷tanα·cotα=1

锟斤拷锟斤拷sinα·cscα=1

锟斤拷锟斤拷cosα·secα=1

锟斤拷锟斤拷锟絁锟斤拷锟斤拷锟角猴拷锟斤拷(sh锟斤拷)锟斤拷式

锟斤拷锟斤拷锟缴角猴拷锟絚锟斤拷锟斤拷锟斤拷呛锟斤拷锟�(sh锟斤拷)锟斤拷

锟斤拷锟斤拷sin(A+B) = sinAcosB+cosAsinB

锟斤拷锟斤拷sin(A-B) = sinAcosB-cosAsinB ?

锟斤拷锟斤拷cos(A+B) = cosAcosB-sinAsinB

锟斤拷锟斤拷cos(A-B) = cosAcosB+sinAsinB

锟斤拷锟斤拷tan(A+B) = (tanA+tanB)/(1-tanAtanB)

锟斤拷锟斤拷tan(A-B) = (tanA-tanB)/(1+tanAtanB)

锟斤拷锟斤拷cot(A+B) = (cotAcotB-1)/(cotB+cotA)

锟斤拷锟斤拷cot(A-B) = (cotAcotB+1)/(cotB-cotA)

锟斤拷锟斤拷锟斤拷锟角和碉拷锟斤拷锟角猴拷锟斤拷(sh锟斤拷)锟斤拷

锟斤拷锟斤拷sin(α+β+γ)=sinα·cosβ·cosγ+cosα·sinβ·cosγ+cosα·cosβ·sinγ-sinα·sinβ·sinγ

锟斤拷锟斤拷cos(α+β+γ)=cosα·cosβ·cosγ-cosα·sinβ·sinγ-sinα·cosβ·sinγ-sinα·sinβ·cosγ

锟斤拷锟斤拷tan(α+β+γ)=(tanα+tanβ+tanγ-tanα·tanβ·tanγ)/(1-tanα·tanβ-tanβ·tanγ-tanγ·tanα)

锟斤拷锟斤拷锟給锟斤拷锟角癸拷式锟斤拷

锟斤拷锟斤拷Asinα+Bcosα=(A^2+B^2)^(1/2)sin(α+t)锟斤拷锟斤拷锟斤拷

锟斤拷锟斤拷sint=B/(A^2+B^2)^(1/2)

锟斤拷锟斤拷cost=A/(A^2+B^2)^(1/2)

锟斤拷锟斤拷tant=B/A

锟斤拷锟斤拷Asinα+Bcosα=(A^2+B^2)^(1/2)cos(α-t)锟斤拷tant=A/B

锟斤拷锟斤拷锟斤拷锟角癸拷式锟斤拷

锟斤拷锟斤拷sin(2α)=2sinα·cosα=2/(tanα+cotα)

锟斤拷锟斤拷cos(2α)=cos^2(α)-sin^2(α)=2cos^2(α)-1=1-2sin^2(α)

锟斤拷锟斤拷tan(2α)=2tanα/[1-tan^2(α)]

锟斤拷锟斤拷锟斤拷锟斤拷锟角癸拷式锟斤拷

锟斤拷锟斤拷sin(3α)=3sinα-4sin^3(α)

锟斤拷锟斤拷cos(3α)=4cos^3(α)-3cosα

锟斤拷锟斤拷锟斤拷枪锟绞斤拷锟�

锟斤拷锟斤拷sin(α/2)=±√((1-cosα)/2)

锟斤拷锟斤拷cos(α/2)=±√((1+cosα)/2)

锟斤拷锟斤拷tan(α/2)=±√((1-cosα)/(1+cosα))=sinα/(1+cosα)=(1-cosα)/sinα

锟斤拷锟斤拷锟斤拷锟界公式锟斤拷

锟斤拷锟斤拷sin^2(α)=(1-cos(2α))/2=versin(2α)/2

锟斤拷锟斤拷cos^2(α)=(1+cos(2α))/2=covers(2α)/2

锟斤拷锟斤拷tan^2(α)=(1-cos(2α))/(1+cos(2α))

锟斤拷锟斤拷锟絝锟杰癸拷式锟斤拷

锟斤拷锟斤拷sinα=2tan(α/2)/[1+tan^2(α/2)]

锟斤拷锟斤拷cosα=[1-tan^2(α/2)]/[1+tan^2(α/2)]

锟斤拷锟斤拷tanα=2tan(α/2)/[1-tan^2(α/2)]

锟斤拷锟斤拷锟絜锟斤拷锟酵差公式锟斤拷

锟斤拷锟斤拷sinα·cosβ=(1/2)[sin(α+β)+sin(α-β)]

锟斤拷锟斤拷cosα·sinβ=(1/2)[sin(α+β)-sin(α-β)]

锟斤拷锟斤拷cosα·cosβ=(1/2)[cos(α+β)+cos(α-β)]

锟斤拷锟斤拷sinα·sinβ=-(1/2)[cos(α+β)-cos(α-β)]

锟斤拷锟斤拷锟酵差化锟絜锟斤拷式锟斤拷

锟斤拷锟斤拷sinα+sinβ=2sin[(α+β)/2]cos[(α-β)/2]

锟斤拷锟斤拷sinα-sinβ=2cos[(α+β)/2]sin[(α-β)/2]

锟斤拷锟斤拷cosα+cosβ=2cos[(α+β)/2]cos[(α-β)/2]

锟斤拷锟斤拷cosα-cosβ=-2sin[(α+β)/2]sin[(α-β)/2]

锟斤拷锟斤拷锟狡岋拷(d锟斤拷o)锟斤拷式锟斤拷

锟斤拷锟斤拷tanα+cotα=2/sin2α

锟斤拷锟斤拷tanα-cotα=-2cot2α

锟斤拷锟斤拷1+cos2α=2cos^2α

锟斤拷锟斤拷1-cos2α=2sin^2α

锟斤拷锟斤拷1+sinα=(sinα/2+cosα/2)^2

锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷

锟斤拷锟斤拷sinα+sin(α+2π/n)+sin(α+2π*2/n)+sin(α+2π*3/n)+……+sin[α+2π*(n-1)/n]=0

锟斤拷锟斤拷cosα+cos(α+2π/n)+cos(α+2π*2/n)+cos(α+2π*3/n)+……+cos[α+2π*(n-1)/n]=0 锟皆硷拷

锟斤拷锟斤拷sin^2(α)+sin^2(α-2π/3)+sin^2(α+2π/3)=3/2

锟斤拷锟斤拷tanAtanBtan(A+B)+tanA+tanB-tan(A+B)=0

锟斤拷锟斤拷锟斤拷锟斤拷(sh锟斤拷)锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟�

锟斤拷锟斤拷锟斤拷平锟斤拷直锟斤拷锟斤拷锟斤拷系xOy锟叫ｏ拷锟斤拷锟絚O锟斤拷锟斤拷一锟絣锟戒線OP锟斤拷锟絆(sh锟斤拷)锟斤拷锟紻(zhu锟斤拷n)锟角烇拷θ锟斤拷锟絆(sh锟斤拷)OP=r锟斤拷P锟絚锟斤拷锟斤拷锟剿烇拷(x锟斤拷y)锟斤拷

锟斤拷锟斤拷锟斤拷锟揭猴拷锟斤拷(sh锟斤拷) sinθ=y/r

锟斤拷锟斤拷锟斤拷锟揭猴拷锟斤拷(sh锟斤拷) cosθ=x/r

锟斤拷锟斤拷锟斤拷锟叫猴拷锟斤拷(sh锟斤拷) tanθ=y/x

锟斤拷锟斤拷锟斤拷锟叫猴拷锟斤拷(sh锟斤拷) cotθ=x/y

锟斤拷锟斤拷锟斤拷锟筋函锟斤拷(sh锟斤拷) secθ=r/x

锟斤拷锟斤拷锟斤拷詈拷锟�(sh锟斤拷) cscθ=r/y

锟斤拷锟斤拷锟斤拷锟斤拷(sin):锟斤拷α锟侥岋拷邊锟斤拷锟斤拷斜邊

锟斤拷锟斤拷锟斤拷锟斤拷(cos):锟斤拷α锟斤拷锟斤拷邊锟斤拷锟斤拷斜邊

锟斤拷锟斤拷锟斤拷锟斤拷(tan):锟斤拷α锟侥岋拷邊锟斤拷锟斤拷锟斤拷邊

锟斤拷锟斤拷锟斤拷锟斤拷(cot):锟斤拷α锟斤拷锟斤拷邊锟斤拷锟较岋拷邊

锟斤拷锟斤拷锟斤拷锟斤拷(sec):锟斤拷α锟斤拷斜邊锟斤拷锟斤拷锟斤拷邊

锟斤拷锟斤拷锟斤拷锟�(csc):锟斤拷α锟斤拷斜邊锟斤拷锟较岋拷邊

锟斤拷锟斤拷锟斤拷锟角猴拷锟斤拷(sh锟斤拷)锟絝锟杰癸拷式

锟斤拷锟斤拷锟絝锟杰癸拷式

锟斤拷锟斤拷(1)(sinα)^2+(cosα)^2=1

锟斤拷锟斤拷(2)1+(tanα)^2=(secα)^2

锟斤拷锟斤拷(3)1+(cotα)^2=(cscα)^2

锟斤拷锟斤拷锟紺锟斤拷锟斤拷锟斤拷锟绞�,只锟借將一式,锟斤拷锟斤拷同锟斤拷(sinα)^2,锟节讹拷锟斤拷锟斤拷(cosα)^2锟斤拷锟斤拷

锟斤拷锟斤拷(4)锟斤拷锟斤拷锟斤拷锟斤拷锟街憋拷锟斤拷锟斤拷锟斤拷锟�,锟斤拷锟斤拷

锟斤拷锟斤拷tanA+tanB+tanC=tanAtanBtanC

锟斤拷锟斤拷锟紺:

锟斤拷锟斤拷A+B=π-C

锟斤拷锟斤拷tan(A+B)=tan(π-C)

锟斤拷锟斤拷(tanA+tanB)/(1-tanAtanB)=(tanπ-tanC)/(1+tanπtanC)

锟斤拷锟斤拷锟斤拷锟斤拷锟缴碉拷

锟斤拷锟斤拷tanA+tanB+tanC=tanAtanBtanC

锟斤拷锟斤拷锟斤拷锟紺

锟斤拷锟斤拷同锟接匡拷锟皆碉拷锟紺,锟斤拷x+y+z=nπ(n∈Z)锟絩,該锟絇(gu锟斤拷n)系式也锟斤拷锟斤拷

锟斤拷锟斤拷锟斤拷tanA+tanB+tanC=tanAtanBtanC锟缴得筹拷锟斤拷锟铰結(ji锟斤拷)論

锟斤拷锟斤拷(5)cotAcotB+cotAcotC+cotBcotC=1

锟斤拷锟斤拷(6)cot(A/2)+cot(B/2)+cot(C/2)=cot(A/2)cot(B/2)cot(C/2)

锟斤拷锟斤拷(7)(cosA)^2+(cosB)^2+(cosC)^2=1-2cosAcosBcosC

锟斤拷锟斤拷(8)(sinA)^2+(sinB)^2+(sinC)^2=2+2cosAcosBcosC

锟斤拷锟斤拷锟絝锟杰癸拷式锟介：

锟斤拷锟斤拷锟絆(sh锟斤拷)tan(A/2)=t

锟斤拷锟斤拷sinA=2t/(1+t^2) (A≠2kπ+π锟斤拷k∈Z)

锟斤拷锟斤拷tanA=2t/(1-t^2) (A≠2kπ+π锟斤拷k∈Z)

锟斤拷锟斤拷cosA=(1-t^2)/(1+t^2) (A≠2kπ+π锟斤拷锟斤拷A≠kπ+(π/2) k∈Z)

锟斤拷锟斤拷锟斤拷锟斤拷锟絝sinA.tanA.cosA锟斤拷锟斤拷锟斤拷锟斤拷tan(A/2)锟斤拷锟斤拷示,锟斤拷要锟斤拷一锟斤拷锟斤拷锟斤拷(sh锟斤拷)式锟斤拷值锟侥時锟斤拷,锟酵匡拷锟斤拷锟斤拷锟絝锟杰癸拷式,锟狡岋拷(d锟斤拷o)锟斤拷只锟斤拷锟斤拷一锟斤拷變锟斤拷锟侥猴拷锟斤拷(sh锟斤拷),锟斤拷值锟酵很猴拷锟斤拷锟斤拷.

锟斤拷锟斤拷锟斤拷锟角猴拷锟斤拷(sh锟斤拷)锟絇(gu锟斤拷n)系

锟斤拷锟斤拷锟斤拷锟斤拷(sh锟斤拷)锟絇(gu锟斤拷n)系

锟斤拷锟斤拷tanα ·cotα=1

锟斤拷锟斤拷sinα ·cscα=1

锟斤拷锟斤拷cosα ·secα=1

锟斤拷锟斤拷锟教碉拷锟絇(gu锟斤拷n)系

锟斤拷锟斤拷sinα/cosα=tanα=secα/cscα

锟斤拷锟斤拷cosα/sinα=cotα=cscαcα

锟斤拷锟斤拷平锟斤拷锟絇(gu锟斤拷n)系

锟斤拷锟斤拷sin^2(α)+cos^2(α)=1

锟斤拷锟斤拷1+tan^2(α)=sec^2(α)

锟斤拷锟斤拷1+cot^2(α)=csc^2(α)

锟斤拷锟斤拷同锟斤拷锟斤拷锟角猴拷锟斤拷(sh锟斤拷)锟絇(gu锟斤拷n)系锟斤拷锟斤拷锟斤拷記锟斤拷锟斤拷

锟斤拷锟斤拷锟斤拷(g锟斤拷u)锟斤拷锟斤拷"锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟铰革拷;锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟絞1"锟斤拷锟斤拷锟斤拷邊锟轿烇拷模锟斤拷锟斤拷

锟斤拷锟斤拷锟斤拷锟斤拷(sh锟斤拷)锟絇(gu锟斤拷n)系

锟斤拷锟斤拷锟斤拷锟角撅拷锟较兩傦拷锟斤拷锟斤拷(sh锟斤拷)锟斤拷锟介倒锟斤拷(sh锟斤拷);

锟斤拷锟斤拷锟教旓拷(sh锟斤拷)锟絇(gu锟斤拷n)系

锟斤拷锟斤拷锟斤拷邊锟斤拷锟斤拷锟斤拷一锟斤拷c锟较的猴拷锟斤拷(sh锟斤拷)值锟斤拷锟斤拷锟絚锟斤拷锟斤拷锟斤拷锟侥兩傦拷锟斤拷c锟较猴拷锟斤拷(sh锟斤拷)值锟侥乘積锟斤拷(锟斤拷要锟角兩條虛锟斤拷锟缴端碉拷锟斤拷锟角猴拷锟斤拷(sh锟斤拷)值锟侥乘積锟斤拷锟斤拷锟斤拷4锟斤拷也锟斤拷锟斤拷锟紷锟絅锟絇(gu锟斤拷n)系锟斤拷)锟斤拷锟缴此ｏ拷锟缴碉拷锟教旓拷(sh锟斤拷)锟絇(gu锟斤拷n)系式锟斤拷

锟斤拷锟斤拷平锟斤拷锟絇(gu锟斤拷n)系

锟斤拷锟斤拷锟节庯拷锟斤拷锟接帮拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟�锟斤拷锟斤拷锟斤拷蓚锟斤拷锟絚锟较碉拷锟斤拷锟角猴拷锟斤拷(sh锟斤拷)值锟斤拷平锟斤拷锟酵碉拷锟斤拷锟斤拷锟斤拷锟斤拷c锟较碉拷锟斤拷锟角猴拷锟斤拷(sh锟斤拷)值锟斤拷平锟斤拷锟斤拷

锟斤拷锟斤拷锟缴角和差公式

锟斤拷锟斤拷sin(α+β)=sinαcosβ+cosαsinβ

锟斤拷锟斤拷sin(α-β)=sinαcosβ-cosαsinβ

锟斤拷锟斤拷cos(α+β)=cosαcosβ-sinαsinβ

锟斤拷锟斤拷cos(α-β)=cosαcosβ+sinαsinβ

锟斤拷锟斤拷tan(α+β)=(tanα+tanβ )/(1-tanα ·tanβ)

锟斤拷锟斤拷tan(α-β)=(tanα-tanβ)/(1+tanα ·tanβ)

锟斤拷锟斤拷锟斤拷锟斤拷锟角碉拷锟斤拷锟斤拷锟斤拷锟斤拷锟揭猴拷锟斤拷锟叫癸拷式

锟斤拷锟斤拷sin2α=2sinαcosα

锟斤拷锟斤拷cos2α=cos^2(α)-sin^2(α)=2cos^2(α)-1=1-2sin^2(α)

锟斤拷锟斤拷tan2α=2tanα/(1-tan^2(α)