шпаргалка по тригонометрии
учебно-методическое пособие (алгебра) по теме

=

=

=

cos (α +β)= –

=

= +

cos (α +β)= –

= (+)/ (1 - )

= +

= ( - 1)/ ( + )

= (+)/ (1 - )

= ( + 1)/ ( - )

= ( - 1)/ ( + )

 = cos2 α– sin2 α = 2cos2 α– 1 = 1- 2sin2α

= ( + 1)/ ( - )

= 2

 = cos2 α– sin2 α = 2cos2 α– 1 = 1- 2sin2α

tg 2α= 2 tgα/ (1 - tg2α)

= 2

ctg2α = (ctg2α – 1)/ 2ctgα

tg 2α= 2 tgα/ (1 - tg2α)

sin3α = 3sinα – 4 sin3α

ctg2α = (ctg2α – 1)/ 2ctgα

cos3α = 4cos3α – 3cosα

sin3α = 3sinα – 4 sin3α

tg3α = (3tgα – tg3α)/ (1 – 3tg2α)

cos3α = 4cos3α – 3cosα

ctg3α = (3ctgα – ctg3α)/ (1 – 3ctg2α)

tg3α = (3tgα – tg3α)/ (1 – 3tg2α)

sin2 = (1 – cosα)/ 2

ctg3α = (3ctgα – ctg3α)/ (1 – 3ctg2α)

cos2 = 1 + cosα)/2

sin2 = (1 – cosα)/ 2

tg 2  = (1 – cosα)/(1+ cos α)

cos2 = 1 + cosα)/2

 tg= sinα/( 1 + cosα) = ( 1 – cos α)/sinα

tg 2  = (1 – cosα)/(1+ cos α)

ctg  = (1  + cosα)/sinα = sinα/ (1 – cosα)

 tg= sinα/( 1 + cosα) = ( 1 – cos α)/sinα

sin α + sin β = 2 sin cos

ctg  = (1  + cosα)/sinα = sinα/ (1 – cosα)

sin α– sin β = 2sincos

sin α + sin β = 2 sin cos

cos α + cos β= 2coscos

sin α– sin β = 2sincos

cos α– cos β = -2sinsin

cos α + cos β= 2coscos

sin α + cos α = sin (α +π/4) = cos (π/4 – α)

cos α– cos β = -2sinsin

a sinαb cosα= sin(α ψ),ψ= arctg

sin α + cos α = sin (α +π/4) = cos (π/4 – α)

tg α + tg β = sin (α + β) / cos α cos β

a sinαb cosα= sin(α ψ),ψ= arctg

tg α – tg β = sin (α – β) / cos α cos β

tg α + tg β = sin (α + β) / cos α cos β

ctg α + ctg β= sin ( α + β) / sinα sinβ

tg α – tg β = sin (α – β) / cos α cos β

ctg α – ctg β = sin (β– α) / sin α sin β

ctg α + ctg β= sin ( α + β) / sinα sinβ

tg α + tg β = cos ( α – β) / cos α sinβ

ctg α – ctg β = sin (β– α) / sin α sin β

tg α – ctgβ = - cos (α +β) / cosα sin β

tg α + tg β = cos ( α – β) / cos α sinβ

tg α+ ctg α= 2 /sin 2α

tg α – ctgβ = - cos (α +β) / cosα sin β

tg α – ctg α = -2 ctg 2α

tg α+ ctg α= 2 /sin 2α

sin α sin β =

tg α – ctg α = -2 ctg 2α

cosα cosβ =

sin α sin β =

sinαcosβ =

cosα cosβ =

sin2α = 2tgα/ (1 + tg2α)

sinαcosβ =

cos2α = (1 – tg2α)/(1 + tg2α)

sin2α = 2tgα/ (1 + tg2α)

sin4α + cos4α = 1 - sin22α

cos2α = (1 – tg2α)/(1 + tg2α)

sin6α + cos6α = 1 -  ( 1 – cos22α)

sin4α + cos4α = 1 - sin22α

tg3α = tgα tg(60– α)tg(60 +α)

sin6α + cos6α = 1 -  ( 1 – cos22α)

sin3α = 4sinα sin(60 – α)sin(60 +α)

tg3α = tgα tg(60– α)tg(60 +α)

cos3α = 4cosα cos(60 – α)cos(60 +α)

sin3α = 4sinα sin(60 – α)sin(60 +α)

cos3α = 4cosα cos(60 – α)cos(60 +α)