arcsin(-x)=-arcsinx arcos(-x)= π- arccosx

jsin²α + cos²α = 1

tgα = sinα / cosα

ctgα = cosα / sinα

tgα ctgα = 1

1 + tg²α =

1 + ctg²α =

sinα ± sinβ = 2sin cos

cosα + cosβ = 2cos cos

cosα − cosβ = 2sin sin

tgα ± tgβ = sin(α ± β) / cosαcosβ

sin(α ± β) = sinαcosβ ± sinβcosα

cos(α β) = cosαcosβ sinαsinβ

tg(α β) = (tgα tgβ) / (1 tgαtgβ)

ctg(α + β) = (ctgα ctgβ - 1) / (ctgα + ctgβ)

ctg(α – β) = (ctgα ctgβ + 1) / (ctgb- ctga)

sinα sinβ = (cos(α − β) – cos(α + β))

sinα cosβ = (sin(α + β) + sin(α − β))

cosα cosβ = (cos(α + β) + cos(α − β))

sin2α = 2sinαcosα

cos2α = cos²α – sin²α

cos2α = 2cos²α – 1

cos2α = 1 – 2sin²α

tg2α = 2tgα / (1 – tg²α)

sin3α = sinα (3 – 4sin²α)

cos3α = cosα (4cos²α – 3)

sin

cos

sin = ± cos = ±

tg = = ±

arcsin x + arccos x = π/2

arctg x + arcctg x = π/2

arcsin x =	{	arccos , 0≤x≤1
− arccos ,−1≤x≤0

arcctg = arctg x, x≠0

arcsin x = arctg , −1<x<1

sin²α = (1 – cos2α) / 2

cos²α = (1 + cos2α) / 2

1 + cosα = 2cos²

1 – cosα = 2sin²

= ,

sinα= tgα=

cosα=

sin x=a

x=(-1)ⁿarcsin a+πn, n Z

cos x=a

x= ± arccos a+2πn, n Z

tg x=a

x=arctg a+πn, n Z

(sin x)′ = cos x (cos x)′= - sin x

(tg x)′ = (ctg x)′ = -

(arcsin x)′ = 1/

(arccos x)′ = −1/

(arctg x)′ = 1 / (1 + x²)

(arcctg x)′ = −1 / (1 + x²)

arcsin(-x)=-arcsinx arcos(-x)= π- arccosx

arctg(-x)=-arctgx arcctg(-x)=π-arcctgx

Дата добавления: 2015-08-29