0

30

45

60

90

Sin

0

1/2

˝(sqrt2)

˝(sqrt3)

1

cos

1

˝(sqrt3)

˝(sqrt2)

˝

0

Tg

0

1/3(sqrt3)

1

Sqrt3

∞

Ctg

∞

Sqrt3

1

1/3(sqrt3)

0

Sin^2 --> [Author:MP] α+cos^2α=1 tgαctgα=1 sinα/cosα=tgα

tgα=sinα/(sqrt(1-sin2α))=(sqrt(1-cos^2α))/cosα

sin(α+β)=sinαcosβ+cosαsinβ

cos(α+β)=cosαcosβ+sinαsinβ

tg(α+β)=(tgα+tgβ)/(1+tgαtgβ)

ctg(α+β)=(ctgαctgβ+1)/(ctgα+ctgβ)

sin2α=2sinαcosα

cos2α=cos^2α-sin^2α=2cos^2α-1=1-2sin^2α

sin3α=3sinα-4sin^3α cos3α=4cos^3α-3cosα

tg2α=(2tgα)/(1-tg^2α) tg3α=(3tgα-tg^3α)/(1-3tg^2α)

ctg2α=(ctg^2α-1)/(2ctgα) ctg3α=(ctg^3α-3ctgα)/(3ctg^2α-1)

sin1/2α=sqrt((1-cosα)/2) cos1/2α=sqrt((1+cosα)/2)

tg1/2α=sqrt((1-cosα)/(1+cosα))=(1-cosα)/sinα=(sinα)/(1+cosα)

ctg1/2α=sqrt((1+cosα)/(1-cosα))=(1+cosα)/sinα=sinα/(1-cosα)

sinα+sinβ=2sin((α+β)/2)cos((α-β)/2)

sinα-sinβ=2cos((α+β)/2)sin((α-β)2)

cosα+cosβ=2cos((α+β)/2)cos((α-β)/2)

cosα-cosβ=-2sin((α+β)/2)sin((α-β)/2)

tgα+tgβ=(sin(α+β))/cosαcosβ ctgα+ctgβ=+(sin(α+β))/sinαsinβ

tgα+ctgβ=(cos(α-β))/cosαsinβ ctgα-tgβ=(cos(α+β))/sinαcosβ

sinαsinβ=1/2(cos(α-β)-cos(α+β)) cosαcosβ=1/2(cos(α-β)+cos(α+β))

sinαcosβ=1/2(sin(α-β)+sin(α+β))

sin^2α=1/2(1-cos2α) cos^2α=1/2(1+cos2α)

sin^3α=1/4(3sinα-sin3α) cos^3α=1/4(cos3α+3cosα)

1+cosα=2cos^21/2α 1-cosα=2sin^21/2α

1+sinα=2cos^2(1/4π-1/2α)=2sin^2(1/4π+1/2α)

1-sinα=2sin^2(1/4π-1/2α)=2cos^2(1/4π+1/2α)

0

30

45

60

90

Sin

0

1/2

˝(sqrt2)

˝(sqrt3)

1

cos

1

˝(sqrt3)

˝(sqrt2)

˝

0

Tg

0

1/3(sqrt3)

1

Sqrt3

∞

Ctg

∞

Sqrt3

1

1/3(sqrt3)

0

Sin^2 --> [Author:MP] α+cos^2α=1 tgαctgα=1 sinα/cosα=tgα

tgα=sinα/(sqrt(1-sin2α))=(sqrt(1-cos^2α))/cosα

sin(α+β)=sinαcosβ+cosαsinβ

cos(α+β)=cosαcosβ+sinαsinβ

tg(α+β)=(tgα+tgβ)/(1+tgαtgβ)

ctg(α+β)=(ctgαctgβ+1)/(ctgα+ctgβ)

sin2α=2sinαcosα

cos2α=cos^2α-sin^2α=2cos^2α-1=1-2sin^2α

sin3α=3sinα-4sin^3α cos3α=4cos^3α-3cosα

tg2α=(2tgα)/(1-tg^2α) tg3α=(3tgα-tg^3α)/(1-3tg^2α)

ctg2α=(ctg^2α-1)/(2ctgα) ctg3α=(ctg^3α-3ctgα)/(3ctg^2α-1)

sin1/2α=sqrt((1-cosα)/2) cos1/2α=sqrt((1+cosα)/2)

tg1/2α=sqrt((1-cosα)/(1+cosα))=(1-cosα)/sinα=(sinα)/(1+cosα)

ctg1/2α=sqrt((1+cosα)/(1-cosα))=(1+cosα)/sinα=sinα/(1-cosα)

sinα+sinβ=2sin((α+β)/2)cos((α-β)/2)

sinα-sinβ=2cos((α+β)/2)sin((α-β)2)

cosα+cosβ=2cos((α+β)/2)cos((α-β)/2)

cosα-cosβ=-2sin((α+β)/2)sin((α-β)/2)

tgα+tgβ=(sin(α+β))/cosαcosβ ctgα+ctgβ=+(sin(α+β))/sinαsinβ

tgα+ctgβ=(cos(α-β))/cosαsinβ ctgα-tgβ=(cos(α+β))/sinαcosβ

sinαsinβ=1/2(cos(α-β)-cos(α+β)) cosαcosβ=1/2(cos(α-β)+cos(α+β))

sinαcosβ=1/2(sin(α-β)+sin(α+β))

sin^2α=1/2(1-cos2α) cos^2α=1/2(1+cos2α)

sin^3α=1/4(3sinα-sin3α) cos^3α=1/4(cos3α+3cosα)

1+cosα=2cos^21/2α 1-cosα=2sin^21/2α

1+sinα=2cos^2(1/4π-1/2α)=2sin^2(1/4π+1/2α)

1-sinα=2sin^2(1/4π-1/2α)=2cos^2(1/4π+1/2α)