Matematikadagi xaridorlar - matematikadan imtihon uchun imtihonga tayyorgarlik ko'rish uchun

Imtihonlarni hech qanday muammosiz topshirishga yordam beradigan matematika xiyoni.

Tarkib

Imtihoni imtihon xiyonatlari

Ekspertiza Cheat choyshablari:

Geometriya

Trigonometriya:	$\sin A = \frac{a}{c}$ $\cos A = \frac{b}{c}$
	$tg A = \frac{\sin A}{\cos A} = \frac{a}{b}$
Kosine teorema:	$c^{2} = a^{2} + b^{2} - 2 a b \cdot \cos C$ $c^{2} = a^{2} + b^{2} - 2 a b \cdot \cos C$
Sinus Teorem:	$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = 2 R$ $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = 2 R$ $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = 2 R$		bu erda r doiraning radiusi
Aylananing tenglamasi:	${(x - x_{0})}^{2} + {(y - y_{0})}^{2} = R^{2}$ ${(x - x_{0})}^{2} + {(y - y_{0})}^{2} = R^{2}$	qayerda $(x_{0}; y_{0})$ Aylana markazining koordinatalari
O'rnatilgan va markaziy burchaklarning nisbati:	$β = \frac{α}{2} = \frac{\cup α}{2}$
Ta'rif doirasi, uchburchak:	$R = \frac{a b c}{4 S}$		Shuningdek, sinuslarning nazariyasini ham ko'ring. Markazda perpendikulyarlar chorrahasida yotadi.
O'rnatilgan doiralar, uchburchak:	$r = \frac{S}{p}$		poligonning yarimpierimetri qaerda. Markaz bisektor chorrahasida yotadi.
Ta'rif doirasi, to'rtburchaklar:	$α + γ = β + δ = 180^{\circ}$
Yozilgan doiralar, to'rtburchaklar:	$a + c = b + d$
Bisektress mulk:	$\frac{a}{x} = \frac{b}{y}$
Chiruvchi akkordlar teorema:	$A M \cdot B M = C M \cdot D M$		Ushbu teoremalarni namoyish etish imkoniyatiga ega bo'lishi kerak
Tangens va akkord o'rtasidagi qoram	$α = \frac{1}{2} \cup A B$
Tangens va sekorning teoremasi:	$C M^{2} = A M \cdot B M$
Tangulyar segmentlar teorema:	$A B = A C$

Raqamlar maydoni:

Aylana:	$S = π r^{2}$
Uchburchak:	$S = \frac{1}{2} a h$
Parallelogramma:	$S = a h$
To'rt -ye -erd:	$S = \frac{1}{2} d_{1} d_{2} \sin φ$	Rombrda $φ = 90^{\circ}$
Trapezius:	$S = \frac{a + b}{2} \cdot h$

Ehtimol

Ehtimol A:	$P (A) = \frac{m}{n}$	m - qulay voqealar soni n - voqealar umumiy soni

Voqealar a va b sodir bo'ladi bir vaqtning o'zida	$A \cdot B$
Mustaqil Hamkorlik:	$P (A \cdot B) = P (A) \cdot P (B)$ $P (A \cdot B) = P (A) \cdot P (B)$	Bir voqea (a) ehtimoli boshqa tadbirga bog'liq bo'lmaganda (b)
Qaram Hamkorlik:	$P (A \cdot B) = P (A) \cdot P (B ∣ A)$ $P (A \cdot B) = P (A) \cdot P (B ∣ A)$	$P (B ∣ A)$ - Batahqiq, BU voqea sodir bo'lgan bo'lsa, B voqea ehtimoli

Sodir bo'ladi yoki a, yoki B.	$A + B$
Tushunib bo'lmaydigan Hamkorlik:	$P (A + B) = P (A) + P (B)$ $P (A + B) = P (A) + P (B)$	Ikkala tadbirning boshlanishi ikkalasi bir vaqtning o'zida imkonsiz bo'lsa, i.e. $P (A \cdot B) = 0$
Qo'shma Hamkorlik:	$P (A + B) = P (A) + P (B) - P (A \cdot B)$ $P (A + B) = P (A) + P (B) - P (A \cdot B)$ $P (A + B) = P (A) + P (B) - P (A \cdot B)$	Ikkala tadbir ham bir vaqtning o'zida kelishi mumkin

Funktsiyalar grafikasi, maktabda o'rganilgan funktsiyalar

Funktsiyaning nomi	Funktsiya formulasi	Grafika nomi	Eslatma
Chiziqli	y \u003d kx	To'g'riga	Chiziqli qaramlik - to'g'ridan-to'g'ri mutanosiblik y \u003d kx, qayerda k K. ≠ 0 - mutanosiblik koeffitsienti.
Chiziqli	shilmoq = kx + b.	To'g'riga	Chiziqli qaramlik: koeffitsientlar k K. va b. - har qanday haqiqiy raqamlar. (k K. \u003d 0,5, b. \u003d 1)
Kvadrat	y \u003d x²	Parabola	Kvadrat bog'liqlik: Simmetrik parabola koordinatlarning boshida.
Kvadrat	y \u003d x^n.	Parabola	Kvadrat bog'liqlik: n. - Tabiiy juft soni\u003e 1
Tik	y \u003d x^n.	Kubani parabola	To'liq daraja: n. - Tabiiy trafik raqam\u003e 1
Tik	y \u003d x^1/2	Funktsiya jadvali shilmoq = √ x	Tik bog'liqlik ( x^1/2 = √ x).
Tik	y \u003d k / x	Giperabya	Salbiy darajada ish (1 / x \u003d x^-1). Omkining-mutanosib bog'liqlik. (k K. \u003d 1)
Ko'rsatadigan	shilmoq = a ^x	Ushbu funktsiyaning jadvali	Uchun indikativ funktsiya a \u003e Biri.
Ko'rsatadigan	y \u003d a ^x	Ushbu funktsiyaning jadvali	0 uchun indikatsion funktsiya a \u003cbittasi.
Logarifmik	shilmoq \u003d jurnal _ax	Logarifm funktsiyasi jadvali	Logarifmik funktsiya: a \u003e Biri.
Logarifmik	y \u003d log _ax	Logarifm funktsiyasi jadvali	Logarifmik funktsiyasi: 0 \u003c a \u003cbittasi.
Sinus	shilmoq \u003d GUN x	Sinusoid	Tragonometrik funktsiya Sinus.
Kosin tili	shilmoq \u003d cos x	Kosinusid	Trigonometrik funktsiya - bu kosine.
Tangent	shilmoq \u003d tg x	Tangyoid	Tangenentning trigonometrik funktsiyasi.
Kotangent	shilmoq \u003d Ctg x	Kotangensenoid	Kotangenlarning trigonometrik funktsiyasi.

Ishning formulalari.

ko'paytirish

: taqsimlash

Ishning formulasi

Ish haqida nima deyish mumkin

A \u003d v t

V (ishlash)

V \u003d a: t

t (vaqt)

t \u003d a

Massa formulasi

M (jami massa)

M \u003d m n

M (bitta mavzu massasi)

m \u003d m: n

n (miqdor)

n \u003d m: m

Qiymati formulasi

C (narx)

C \u003d va n

narx haqida nima deyish mumkin

a \u003d c: n

n (miqdor)

n \u003d c: a

Yo'lning formulasi

S (masofa, yo'l)

S \u003d v t

V (tezlik)

V \u003d s: t

t (vaqt)

t \u003d s: v

Maydonning formulasi

S (hudud)

S \u003d a b

S \u003d a a

a (uzunligi)

a \u003d s: b

a \u003d S: a

b (kengligi)

b \u003d s: a

a \u003d S: a

Qoldiq bilan bo'linish formulasi a \u003d b c + r,r B.
Perimetr formula p \u003d a 4 p \u003d (a + b) 2
a \u003d p: 4 (kvadrat tomoni) A \u003d (p - b 2): 2 (to'rtburchakning yon tomoni)
Ovozli formula:
- to'rtburchaklar paralleleped v \u003d a b c (kun, b kenglik, C- balandligi)
a \u003d V: (A b) (to'rtburchaklar paralleleptiplangan)
- Kuba v \u003d a a a a
a \u003d V: (a a) (kubning tomoni)

O'rta maktab o'quvchilari uchun trigonometrik formulalar

Bir burchakning trigonometrik funktsiyalari

Ikki burchakning miqdori va farqning trigonometrik funktsiyalari

Ikki burchakning trigonometrik funktsiyalari

Trigonometrik funktsiyalar uchun kvadratlar uchun darajadagi shakllar

Sinus va kosine kubiklari uchun darajadagi darajadagi formulalara

Sinus va ikki tomonlama burchakli ekish orqali tanang ifodasi

Tragonometrik funktsiyalar miqdorini ishga aylantirish

Tragonometrik funktsiyalar ishini miqdorda o'zgartirish

Tragonometrik funktsiyalarning yarmi tangenent orqali ifodalash

Uchburchak burchakning trigonometrik funktsiyalari

Imtihonga tayyorgarlik ko'rish uchun matematika xiyoni

Imtihonga tayyorgarlik ko'rish uchun matematika xiyosi choyshablari:

Qisqartirilgan ko'paytirish uchun formulalar

(a + b) ² \u003d a ² + 2ab + b ²

(A-B) ² \u003d a ² - 2AB + b ²

a ² - ² \u003d (a-b) (a + b)

a ³ - ³ \u003d (a-b) (a ² + AB + B ²)

a ³ + b ³ \u003d (a + b) (a ² - AB + B ²)

(a + b) ³ \u003d a ³ + 3a ²b + 3ab ²+ b ³

(A - B) ³ \u003d a ³ - 3a ²b + 3ab ²- ³

Darajalarning xususiyatlari

a ⁰ \u003d 1 (a ≠ 0)

a ^{m / n} \u003d (a≥0, n e n, m e n)

a ^{- r} \u003d 1 / a ^r (a\u003e 0, r e)

a ^shodlik · A ^n. \u003d a ^{m + n}

a ^shodlik : a ^n. \u003d a ^{m - n} (a ≠ 0)

(a ^shodlik)^N. \u003d a ^mn

(AB) ^N. \u003d a ^n. B. ^n.

(a / b) ^n. \u003d a ^N.vas ^N.

Birinchi bo'lib -

Agar f '(x) \u003d F (x), keyin f (x) - birlamchi

f (x) uchun

Funktsiyafavqulodda(x) \u003d BirlamchiFavqulodda(x)

k \u003d kx + c

x ^n. \u003d x ^n.⁺¹/ n + 1 + c

1 / x \u003d ln | x | + C..

e. ^x \u003d E ^x + C..

a ^x \u003d a ^x/ ln a + c

1 / √x \u003d 2√ c

cos x \u003d sind x + c

1 / gunoh ² x \u003d - ctg x + c

1 / cos ² x \u003d tg x + c

sin X \u003d - cos x + c

1 / x ² \u003d - 1 / x

Geometrik rivojlanish

b. _n.₊₁ \u003d b _n. · Q, unda n e n

q - Precressiya

b. _n. \u003d b ₁ · Q. ^n.^bir - progressiya a'zosi

So'mn-s a'zolari

S. _n. \u003d (b) _N. Q - B _biri ) / Q-1

S. _n. \u003d b _biri (Savol: ^N. -1) / Q-1

Modul

| A | \u003d a bo'lsa, a

- agar a \u003c0 bo'lsa

Formula Kosva gunoh

sin (-x) \u003d -SIN X

cos (-x) \u003d cos x

gunt (x + p) \u003d -Sin x

cos (x + p) \u003d -cos x

gunt (x + 2pk) \u003d sin x

cos (x + 2pk) \u003d cos x

gunt (x + p / 2) \u003d cos x

Jismlarning hajmi va yuzalari

1. Prizizm, to'g'ri yoki moyil, parallelepipedV \u003d Snki

2. To'g'ridan-to'g'ri prizma S. _Tomon\u003d pname, p perimetri yoki atrofi uzunligi

3. parallelepiped to'rtburchaklar

V \u003d Aburu; P \u003d 2 (ABA B + BAY Á00)

P to'liq yuzasi

4. kub: V \u003d a ³ ; P \u003d 6 a ²

5. Piramida, to'g'ri va noto'g'ri.

S \u003d 1/3 S xu; S - asos

6.Piramida to'g'ri S \u003d 1/2 Plyon

A - to'g'ri piramidaning Apofem

7. Tarmoqli tsilindr V \u003d s · h \u003d mil ²r

8. Tarmoqli tsilindr: S. _Tomon \u003d 2 pRh

9. Dumaloq konus: V \u003d 1/3 sh \u003d 1/3 mil ²r

o'nta. Dumaloq konus:S. _Tomon \u003d 1/2 pl \u003d sill

Trigonometrik tenglamalar

sin x \u003d 0, x \u003d pn

sin x \u003d 1, x \u003d p / 2 + 2 pn

sin x \u003d -1, x \u003dp / 2 + 2 pn

cos x \u003d 0, x \u003d p / 2 + 2 pn

cos x \u003d 1, x \u003d 2p

cos x \u003d -1, x \u003d p + 2 pn

Qo'shimcha teoremalar

cos (x + y) \u003d cosx · qulay

cos (x -y) \u003d Cosx · Sinx · gunohli

gunt (x + y) \u003d Sinx · Cosx · Gony

gunt (x -y) \u003d Sinx · Siny

tg (x ± y) \u003d tg x ± tg y / 1 ^—₊ tg x · tg y

cTG (x ± y) \u003d tg x ^—₊ tg y / 1 ± tg x · tg y

sHIN X ± SHEH Y \u003d 2 Cos (x ± y / 2) kos (x ^—₊y / 2)

cos x ± COCY \u003d 'Sin (x ± Y / 2) Sin (x ^—₊y / 2)

1 + cos 2x \u003d 2 cos ² x; kos ²x \u003d 1 + cos2x / 2

1 - cos 2x \u003d 2 gunoh ² x; gunoh ²x \u003d 1- cos2x / 2

6.Trapezius

a, b - bazalar; h - balandligi, c - S \u003d (A + B / 2) · H He C Y

7.Kvadrat

a - yon, d - diagonal s \u003d a ² \u003d D ²/2

8. Rombbus

a - yon, d ₁, d ₂ - diagonallar, a ular orasidagi burchak s \u003d d ₁d. ₂/ 2 \u003d a ²sindirmoq

9. To'g'ri hexagon

a - yon tomon \u003d (3√3 / 2) a ²

o'nta.Aylana

S \u003d (l / 2) r \u003d mil ² \u003d pd ²/4

o'n bir.Sektor

S \u003d (mil ²/ 360) a

Farqlash qoidalari

(f (x) + g (x) '\u003d x) + g' (x)

(k (f (f (x) '\u003d kf' (x)

(f (x) g (x) '\u003d F' (x) g (x) + F (x) (x) (x)

(f (x) / g (x) '\u003d (x) g (x) g (x) - f (x)) / g ² (x)

(X ^n.) '\u003d Nx ^n-1

(tg x) '\u003d 1 / cos ² x

(CTG x) '\u003d - 1 ² x

(f (kx + m)) '\u003d kf' (KX + M)

Funktsiya grafikasi uchun tangent tenglamasi

y \u003d f '(a) (x-a) + f (a)

KvadratS. Tuzatish bilan cheklangan raqamlarx=a, x=b.

S \u003d ∫ (f (x) - g (x)) Dx

Nyuton formulasi

∫_a^b. f (x) dx \u003d f (b) - F (a)

t p / 4 p / 2 3p π kos √2 / 2 0 --√2 / 2 1 gunoh √2 / 2 1 √2 / 2 0 t 5p 3p 7p / 4 2p kos --√2 / 2 0 √2 / 2 1 gunoh --√2 / 2 -1 --√2 / 2 0 t 0 p / 6 p / 4 p / 3 tg 0 √3 / 3 1 √33 ktg - √3 1 √3 / 3
X \u003d b x \u003d (-1) ^n. Arcsin b + pn

cos x \u003d b x \u003d ± arcos b + 2 pn

tg x \u003d b x \u003d arctg b + pn

cTG X \u003d b X \u003d arcctg b + pn

Teorema sinusov: a / stol a \u003d b / go \u003d c / gr g \u003d 2r
Kosine teorema: Bilan ²\u003d a ²+ b ²-2AB cos y
Integramma

∫ dx \u003d x + c

∫ x ^n. Dx \u003d (x ^n.⁺¹/ n + 1) + c

∫ dx / x ² \u003d -1 / x + c

∫ DX / @ whhh \u003d 2hlh + c

∫ (kx + b) \u003d 1 / k f (kx + b)

∫ Sin X DX \u003d - COS X + C

∫ cos x dx \u003d sind x + c

∫ dx / gol ² x \u003d -ctg + c

∫ dx / cos ² x \u003d tg + c

∫ x ^r Dx \u003d x ^{R + 1}/ r + 1 + c

Logarifmlar

1. Kirish _a A \u003d 1

2. Kirish _a 1 \u003d 0

3. Kirish _a (b ^n.) \u003d n jurnal _a B.

4. Kirish _A^n. b \u003d 1 / n jurnal _a B.

5. Kirish _a B \u003d log _C. B / jurnal _c. a

6. Jurnal _a B \u003d 1 / jurnal _B. a

Daraja 0 30 45 60 gunoh 0 1/2 √2 / 2 √3 / 2 kos 1 √0 / 2 √2 / 2 1/2 tg 0 √3 / 3 1 √33 t p / 6 p / 3 2p 5p kos √3 / 2 1/2 -1/2 --√4 / 2 gunoh 1/2 √3 √3/2 1/2 90 120 135 150 180 1 √0 / 2 √2 / 2 1/2 0/22/2 --√2 / 2 -1 -----2-√3 / 3 0 t 7P / 6 4p 5p 11p kos --√√ / 2 -1/2 1/2 √3 / 2 gunoh -1/2 --√3 / 2 --√4 / 2 -1/2

Ikki marta argument formulalari

cos 2x \u003d cos ²x - gunoh ² x \u003d 2 cos ² X -1 \u003d 1 -2 gunoh ² x \u003d 1 - tg ² X / 1 + TG ² x

sin 2x \u003d 2 Sin X · 1 tg x / 1 tg ²x

tg 2x \u003d 2 tg x / 1 - TG ² x

cTG 2x \u003d CTG ² X - 1/2 CTG x

3x \u003d 3 siniq x - 4 gunoh ³ x

cos 3x \u003d 4 cos ³ x - 3 cos x

tg 3x \u003d 3 tg x - tg ³ X / 1 - 3 TG ² x

sin S Cos t \u003d (Sin (S + T) + Gun (S + T)) / 2

sin S SON T \u003d (COS (S-T) -COS (S + T)) / 2

cos s cos t \u003d (kos (s + t) + cos (s-t)) / 2

Farqlash formulasi

c '\u003d 0 ()' \u003d 1/2

x '\u003d 1 (Sin x)' \u003d cos x

(kx + m) '\u003d k (cos x)' \u003d - Sin X

(1 / x) '\u003d - (1 / x ²) (ln x) '\u003d 1 / x

(E.) ^x) '\u003d E ^x; (X ^n.) '\u003d Nx ^N-1; (jurnal _a x) '\u003d 1 / x ln a a

Yassi raqamlarning kvadratlari

1. To'rtburchaklar uchburchak

S \u003d 1/2 A · b (A, B - so'qmoqlar)

2. izoseles uchburchak

S \u003d (A / 2) · ífiy ² - a ²/4

3. Teng tomonli uchburchak

S \u003d (a ²/ 4) · · íl3 (a-yon)

to'rt.O'zboshimchalik bilan uchburchak

a, B, C - tomoni, a - baza, H balandlik, A, B, C burchaklari yon tomonlarga yotar edi; p \u003d (a + b + c) / 2

S \u003d 1/2 a · h h H h h 1 a ²b Sin C \u003d

a ²sinb Sthens / 2 Sinf A \u003d √ √ (p-b) (p-C)

5. Parallelogramma

a, B tomonlar, a - burchaklardan biri; h - balandlik s \u003d a · H h e lak

cos (x + p / 2) \u003d - xin x

Formula Tgva Ktg

tg x \u003d sind x / cos x; CTG X \u003d COS X / Sin X

tg (-x) \u003d -tg x

cTG (-x) \u003d -ctg x

tg (x + pk) \u003d tg x

cTG (x + pk) \u003d ctg x

tg (x ± p) \u003d ± TG x

cTG (x ± p) \u003d ± ctg x

tg (x + p / 2) \u003d - ctg x

cTG (x + p / 2) \u003d - tg x

gunoh ² X + cos ² x \u003d 1

tg x tg x \u003d 1

1 + tg ² x \u003d 1 / cos ² x

1 + CTG ² x \u003d 1 / gunoh ²x

tg ² (X / 2) \u003d 1 - cos x / 1 cos x

kos ² (X / 2) \u003d 1 + cos x / 2

gunoh ² (X / 2) \u003d 1 - cos x / 2

o'n bir.To'p: V \u003d 4/3 mil ³ \u003d 1/6 chd ³

P \u003d 4 mil ² \u003d pd ²

12.To'p segmenti

V \u003d ph ² (R-1 / 3h) \u003d ph / 6 (H) ² + 3r ²)

S. _Tomon \u003d 2 phh \u003d p (r ² + H ²); P \u003d p (2r ² + H ²)

13.To'p qatlami

V \u003d 1/6 ph ³ + 1/2 p (r ² + H ²· H;

S. _Tomon \u003d 2 p · h

14. Ball sektori:

V \u003d 2/3 mil ² h "h" sektorda bo'lgan segmentning balandligi

Kvadrat tenglama ildizlarining formulasi

(A azeas, bk0)

(a≥0)

bolta ² + bx + c \u003d 0 (a ≠ 0)

Agar d \u003d 0, keyin x \u003d -b / 2a (d \u003d b) ²-4AC)

Agar D\u003e 0 bo'lsa, x _1,2 \u003d -b ± / 2a

Vieta teoremasi

x ₁ + x ₂ \u003d -b / a

x ₁ · X ₂ \u003d C / a

Arifmetik progressiya

a _n.₊₁\u003d a _n. + D, bu tabiiy son

d rivojlanish farqidir;

a _n.\u003d a _biri + (N-1) · D-Formulas

So'm N.a'zolari

S. _n. \u003d (a _biri + a _N. ) / 2) n

S. _n. \u003d ((2a) _biri + (n-1) d) / 2) n

Poligon yaqinidagi tasvirlangan doiralar radiusi

R \u003d a / 2 sinov 180 / n

Birlashgan doiraning radiusi

r \u003d a / 2 tg 180 / n

Aylanmoq

L \u003d 2 pr s \u003d ur ²

Konus maydoni

S. _Tomon \u003d sild

S. _Konus\u003d ur (l + r)

Tangent burchagi- qarama-qarshi oyoqning qo'shniga bo'lgan munosabati. Kotangenlar - aksincha.

Profil matematikadagi podpoller

Ixtisoslashgan matematikada chanqoq:

F-LLA.

sin² Ern / 2 \u003d (1 - Cos ENERN) / 2

cos Ern / 2 \u003d (1 + COVTENT) / 2

tg Ern / 2 \u003d SHANORN / (1 + COSET) \u003d (1-Cos Exer) / Sin ISP

M yp shi ~ li li + 2 n, n ỷ z

F-LI ishlab chiqarish miqdorini o'zgartirish.

sin x + sin y \u003d 2 Sin ((x + y) / 2) cos ((x-y) / 2)

sin X-Sin Y \u003d 2 Cos ((x + y) / 2) GUN ((x-y) / 2)

cos x + cos y \u003d 2cos (x + y) / 2 cos (x-y) / 2

cos x -cos y \u003d -2SIN (x + y) / 2 ta gunoh (x -y) / 2

Formulas Preobr. Ishlab chiqarish. Miqdorda

sinH X Sin y \u003d ½ (Cos (x-y) -cos (x + y))

cos x cos y \u003d ½ (kos (x-y) + cos (x + y))

sin x Cos y \u003d ½ (GUL (X-Y) + Gal (x + y))

Vazifalar orasidagi nisbat

sin X \u003d (2 tg x / 2) / (1 + tg) ²x / 2)

cos x \u003d (1-tg ² 2 / x) / (1+ tg² x / 2)

sin2x \u003d (2tgx) / (1 + tg) ²x)

sin² Ern \u003d 1 / (1 + CTG² Mon) \u003d Tg² Micika / (1 + TG² ISP)

cOS² Ern \u003d 1 / (1 + TG² ISP) \u003d CTG² √ / (1 + CTG² ISP)

cTG2 quvur

sin3 Pipes \u003d 3Sinorn -4Sin³ √ \u003d 3cos ther chirin chirin - deby³

cos3p \u003d 4cos³ Š -3 coss \u003d cos eŠ -3cosporn ml

tg3mer \u003d (3tgper-stgu m) / (1-3tg² m)

cTG3P \u003d (CTG³ ISPG fabrikasi) / (3CTG² ISP)

sin Ern / 2 \u003d   ((1 ta model) / 2)

cos Ern / 2 \u003d   ((1 sxelp) / 2)

tHHP / 2 \u003d   ((1 sielys) / (1 + Cohp) \u003d

sinorn / (1 + kovati) \u003d (1 ta model) / gunoh qilish

cTG fall tegirmoni / 2 \u003d   ((1 + kazim) / (1-kosmet) \u003d

sHINORN / (COSCOCOMI) \u003d (1 + COSETT) / GAS

gunt (arcsin ISP) \u003d ₽

cos (arccos ISP) \u003d ₽

tg (arctg ISP) \u003d ₽

cTG (arcctg ISP) \u003d ₽

arcsin (Sinoff) \u003d Ern; M ↓ [  / 2]

arccos (COS ISP) \u003d EŠ;   [0; ]

arctg (tg ISP) \u003d √; M ↓ [  / 2]

arcctg (CTG ISP) \u003d ₽;   [0; ]

arxsin (gunoh) )=

ISP - 2 k; ① ② [- / 2 + 2 k;  / 2 + 2 k]

(2k + 1)  - ISP; § [ / 2 + 2 k; 3 / 2 + 2 k]

arccos (cos ) =

M -2 k; M  [2 dona; (2k + 1) ]

2 k ca; § [(2k-1) ; 2 k]

arctg (tg )=  — K K.

M  (-Bu / 2 +  k;  / 2 +  k)

arcctg (CTG ) =  — K K.

M  ( k; (K + 1) )

arcsinorn \u003d -csin (-FSIN (-FONS) \u003d  / 2-arcosoff \u003d

\u003d arctg il /  (1-PAN ²)

arccosoff \u003d  -CCCOS (-M) \u003d  / 2-Assasin Ern \u003d

\u003d a arc ctg quvurlari /  (1-PAN ²)

arctgovern \u003d -m) \u003d  / 2 -CCTTG PAN \u003d

\u003d arcsin Ern /  (1 +  ²)

arc ctg √ \u003d  -Car cctg (-F) \u003d

\u003d aRC cos mon /  (1-PAN ²)

arctg ern \u003d arc ctg1 / √ \u003d

\u003d arcsin Ern /  (1 +  ²) \u003d arkcos1 /  (1 + ISP)

arcsin Ern + arccos \u003d  / 2

arcctg nern + arctg tokes \u003d  / 2

Ko'rsatkichli tenglamalar.

Tengsizlik: agar a bo'lsa ^{f (x)}\u003e (\u003c) A ^{a (h)}

A\u003e 1, belgisi o'zgarmaydi.

A \u003c1, keyin belgi o'zgaradi.

Logarifms: tengsizlik:

jurnal _af (x)\u003e (\u003c) jurnal _a  (x)

1. A\u003e 1, keyin: F (x)\u003e 0

 (x)\u003e 0

f (x)\u003e  (x)

2. 0 \u003ca \u003c1, keyin: \u003d 'F (x) \u003d ""\u003e 0

 (x)\u003e 0

f (x) \u003c (x)

3. Kirish _{f (x)}  (x) \u003d a

ODZ:  (x)\u003e 0

f (x)\u003e 0

f (x)  1

Trigonometriya:

1. Ko'plab ko'paytirgichlarga ajratish:

2x -  3 Cos x \u003d 0

2Sin X Cos x -3 Cos x \u003d 0

cos x (2 siniq x -  3) \u003d 0

2. O'zgartirish bo'yicha echimlar

3.Sin² x - Gal 2x + 3 cosę cos x \u003d 2

sin² X - 2 Sin X Cos x + 3 Cos ² X \u003d 2 Sinę² X COS² X

Keyin agar g \u003d 0, agar Cos x \u003d 0 bo'lsa, u yozilgan.

va bu mumkin emas, \u003d\u003e cos x ga bo'linishi mumkin

Tragonometrik asab:

gunoh  shodlik

2 K + ₁ =  =  ₂+ 2 K K.

2 K + ₂ =  = ( ₁+2 ) + 2 K K.

Misol:

Men cos ( / 8 + x) \u003c 3/2

 k + 5 / 6  / 8 + x \u003c7 / 6 + 2 k

2 k + 17 / 24 \u003cx  / 24 + 2 k ;;;;;;

II GR Sin Ern \u003d 1/2

2 k + 5 / 6 \u003d √ \u003d 13 / 6 + 2 k

kos  (= ) m

2 K + ₁ <  <  ₂+2 K K.

2 K + ₂<  < ( ₁+2 ) + 2 K K.

cos Mon  -  2/2

2 k + 5 / 4 \u003d √ \u003d 11 / 4 + 2 k

tg  (= ) m

 K + arctg m=  = Arctg m + K K.

ktg (= ) m

 K + arcctg m \u003c <  + K K.

Integratsiyalar:

 x ^n.dx \u003d x ^{n + 1}/ (n + 1) + c

 a ^xdx \u003d bob / ln a + c

 e ^x Dx \u003d e ^x + C..

 Cos x DX \u003d Sin X + Cos

 Sin X DX \u003d - COS X + C

 1 / x dx \u003d ln | x | + C..

 1 / COS² X \u003d TG x + C

 1 / Sin² X \u003d - CTG X + C

 1 /  (1-x²) dx \u003d arcsin x + c

 1 /  (1-x²) dx \u003d -ccosts x + c

 1/1 + x² dx \u003d arctg x + c

 1/1 + x² dx \u003d - arcctg x + c

Matematikadagi formulalar - rasmlardagi aldash

Matematikadagi formulalar - rasmlar varag'i:

Darslarda maktab o'quvchilariga yordam berish

VIDEO: profil imtihonining birinchi qismidagi aldash varag'i

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