Формулы / формулы

●sin²α+cos²β=1

tgα*ctgβ=1

tg²α+1=1/cos²α

ctg²α+1=1/sin²α

●sinα*sinβ=(cos(α-β)-cos(α+β))

sinα*cosβ=(cos(α-β)+cos(α+β))

cosα*cosβ=(sin(α-β)+sin(α+β))

●cos(α±β)=cosα*cosβsinα*sinβ

sin(α±β)= sinα*cosβ±cosα*sinβ

tg(α±β)=(tgα±tgβ)/(1tgα*tgβ)

ctg(α±β)=(ctgα*ctgβ1)/(ctgα±ctgβ)

●sinα±sinβ=2*sin((α±β)/2)-cos((αβ)/2)

cosα+cosβ=2*cos((α+β)/2)-cos((α-β)/2)

cosα-cosβ=-2*sin((α-β)/2)-sin((α+β)/2)

tgα±tgβ=sin(α±β)/ cosα*cosβ

●sinα*sinβ=-(cos(α+β)-cos(α-β))/2

cosα*cosβ=(cos(α+β)+cos(α-β))/2

+sin

-cos

+sin

+cos

-tg

-ctg

+tg

+ctg

-sin

-cos

-sin

+cos

+tg

+ctg

-tg

-ctg

●sin2α=2sinα*cosα

sin2α=2tgα/(1+tg²α)

cos2α=cos²α-sin²α

cos2α=1-2sin²α

cos2α=2cos²α-1

cos2α=(1-tg²α)/(1+tg²α)

tg2α=2tgα(1-tg²α)

●sin²(α/2)=(1-cosα)/2

cos²(α/2)=(1+cosα)/2

tg(α/2)=sinα/(1+cosα)

tg(α/2)=(1-cosα)/sinα

tg²(α/2)=(1-cosα)/(1+cosα)

α

0

0°

π/6

30°

π/4

45°

π/3

60°

π/2

90°

2π/3

120°

3π/4

135°

5π/6

150°

π

180°

sin

0

½

√2/2

√3/2

1

√3/2

√2/2

√3/3

0

cos

1

√3/2

√2/2

1/2

0

-1/2

-√2/2

-√3

-1

tg

0

√3/3

1

√3

-

-√3

-1

-1/2

0

ctg

-

√3

1

√3/3

0

-√3/3

-1

-√3/2

-

α

7π/6

210°

5π/4

225°

4π/3

240°

3π/2

270°

5π/3

300°

7π/4

315°

11π/6

330°

2π

360°

sin

-1/2

-√2/2

-√3/2

-1

-√3/2

-√2/2

-1/2

0

cos

-√3/2

-√2/2

-1/2

0

1/2

√2/2

√3/2

1

tg

√3/3

1

√3

-

-√3

-1

-√3/3

0

ctg

√3

1

√3/3

0

-√3/3

-1

-√3

-

α

π±α

π±α

π±α

π±α

sin

sin

±sin

cos

-cos

cos

-cos

cos

sin

±sin

tg

±tg

±tg

ctg

ctg

●sin²α+cos²β=1

tgα*ctgβ=1

tg²α+1=1/cos²α

ctg²α+1=1/sin²α

●sinα*sinβ=(cos(α-β)-cos(α+β))

sinα*cosβ=(cos(α-β)+cos(α+β))

cosα*cosβ=(sin(α-β)+sin(α+β))

●cos(α±β)=cosα*cosβsinα*sinβ

sin(α±β)= sinα*cosβ±cosα*sinβ

tg(α±β)=(tgα±tgβ)/(1tgα*tgβ)

ctg(α±β)=(ctgα*ctgβ1)/(ctgα±ctgβ)

●sinα±sinβ=2*sin((α±β)/2)-cos((αβ)/2)

cosα+cosβ=2*cos((α+β)/2)-cos((α-β)/2)

cosα-cosβ=-2*sin((α-β)/2)-sin((α+β)/2)

tgα±tgβ=sin(α±β)/ cosα*cosβ

●sinα*sinβ=-(cos(α+β)-cos(α-β))/2

cosα*cosβ=(cos(α+β)+cos(α-β))/2

+sin

-cos

+sin

+cos

-tg

-ctg

+tg

+ctg

-sin

-cos

-sin

+cos

+tg

+ctg

-tg

-ctg

●sin2α=2sinα*cosα

sin2α=2tgα/(1+tg²α)

cos2α=cos²α-sin²α

cos2α=1-2sin²α

cos2α=2cos²α-1

cos2α=(1-tg²α)/(1+tg²α)

tg2α=2tgα(1-tg²α)

●sin²(α/2)=(1-cosα)/2

cos²(α/2)=(1+cosα)/2

tg(α/2)=sinα/(1+cosα)

tg(α/2)=(1-cosα)/sinα

tg²(α/2)=(1-cosα)/(1+cosα)

α

0

0°

π/6

30°

π/4

45°

π/3

60°

π/2

90°

2π/3

120°

3π/4

135°

5π/6

150°

π

180°

sin

0

½

√2/2

√3/2

1

√3/2

√2/2

√3/3

0

cos

1

√3/2

√2/2

1/2

0

-1/2

-√2/2

-√3

-1

tg

0

√3/3

1

√3

-

-√3

-1

-1/2

0

ctg

-

√3

1

√3/3

0

-√3/3

-1

-√3/2

-

α

7π/6

210°

5π/4

225°

4π/3

240°

3π/2

270°

5π/3

300°

7π/4

315°

11π/6

330°

2π

360°

sin

-1/2

-√2/2

-√3/2

-1

-√3/2

-√2/2

-1/2

0

cos

-√3/2

-√2/2

-1/2

0

1/2

√2/2

√3/2

1

tg

√3/3

1

√3

-

-√3

-1

-√3/3

0

ctg

√3

1

√3/3

0

-√3/3

-1

-√3

-

α

π±α

π±α

π±α

π±α

sin

sin

±sin

cos

-cos

cos

-cos

cos

sin

±sin

tg

±tg

±tg

ctg

ctg

sinα~α

sinα=α

tgα~α

tgα=α

arcsinα~α

arcsinα=α

arctgα~α

arctgα=α

1-cosα~α²/2

1-cosα=α²/2

a^α-1~α lna

a^α-1=α lna

e^α-1~α

e^α-1=α

log_a(1+α) ~α/lna

log_a(1+α)=α/lna

ln(1+α) ~α

ln(1+α)=α

(1+α)ⁿ-1~nα

(1+α)ⁿ-1=nα

(xⁿ)’=nx^n-1

()’=1/(2)

(a^x)’=a^xlna

(e^x)’=e^x

(log_ax)’=

(lnx)’=

(sinx)’=cosx

(shx)’=chx

(cosx)’=-sinx

(chx)’=-shx

(tgx)’=

(thx)’=

(ctgx)’=

(cthx)’=

(arcsinx)’=

(arccosx)’=

(arctgx)’=

(arcctgx)’=

sinα~α

sinα=α

tgα~α

tgα=α

arcsinα~α

arcsinα=α

arctgα~α

arctgα=α

1-cosα~α²/2

1-cosα=α²/2

a^α-1~α lna

a^α-1=α lna

e^α-1~α

e^α-1=α

log_a(1+α) ~α/lna

log_a(1+α)=α/lna

ln(1+α) ~α

ln(1+α)=α

(1+α)ⁿ-1~nα

(1+α)ⁿ-1=nα

(xⁿ)’=nx^n-1

()’=1/(2)

(a^x)’=a^xlna

(e^x)’=e^x

(log_ax)’=

(lnx)’=

(sinx)’=cosx

(shx)’=chx

(cosx)’=-sinx

(chx)’=-shx

(tgx)’=

(thx)’=

(ctgx)’=

(cthx)’=

(arcsinx)’=

(arccosx)’=

(arctgx)’=

(arcctgx)’=