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)

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