Matematika (24.05.2025) 1-smena

45 ta savol · saqlash uchun kiring

Matematika formulalar varaqasi / Лист формул по математике

Tenglamalar / Уравнения

ax^{2}+bx+c=0; \quad x_{1:2}=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}; \quad \begin{cases}x_{1}+x_{2}=-\frac{b}{a}\\ x_{1}\cdot x_{2}=\frac{c}{a}\end{cases}

|f(x)|+|g(x)|=|f(x)+g(x)|\Rightarrow f(x)\cdot g(x)\ge0;

\frac{Ax}{ax^{2}\pm bx-c}\pm\frac{Bx}{ax^{2}\pm dx+c}=k \quad \Rightarrow \quad \frac{A}{ax-\frac{c}{x}\pm b}\pm\frac{B}{ax+\frac{c}{x}\pm d}=k;

(ax^{2}\pm bx-c)(ax^{2}\pm dx+c)=Ax^{2} \quad \Rightarrow \quad (ax-\frac{c}{x}\pm b)(ax+\frac{c}{x}\pm d)=A;

ax+\frac{c}{x}=z

o'zgaruvchi kiritib yechiladi / решается c помошью замены

(x-a)(x-b)(x-c)(x-d) = A \quad \Rightarrow \quad a+b=c+d

bo'lsa,

t=x^{2}-(a+b)x

o'zgaruvchi kiritib yechiladi / решается c помошью замены

Qisqa ko'paytirish formulalari / Формулы сокращённого умножения

a^{2}-b^{2}=(a-b)(a+b)

(a\pm b)^{2}=(a^{2}\pm2ab+b^{2})

(a\pm b)^{3}=a^{3}\pm3a^{2}b+3ab^{2}\pm b^{3}

a^{3}\pm b^{3}=(a\pm b)(a^{2}\mp ab+b^{2})

a^{n}-b^{n}=(a-b)(a^{n-1}+a^{n-2}b+...+ab^{n-2}+b^{n-1})

a^{2n}\pm b^{2n}=(a\pm b)(a^{2n-1}\mp a^{2n-2}b+...+ab^{2n-2}\mp b^{2n-1})

a^{2n+1}\pm b^{2n+1}=(a\pm b)(a^{2n}\mp a^{2n-1}b+...+ab^{2n-1}\mp b^{2n})

(a+b)^{n}=a^{n}+na^{n-1}b+\frac{n(n-1)}{2!}a^{n-2}b^{2}+...

...+\frac{n(n-1)(n-2)\cdot...\cdot(n-(k-1))}{k!}+...+nab^{n-1}+b^{n}

Arifmetik progressiya / Арифметическая прогрессия

a_{n}=a_{n-1}+d=a_{1}+(n-1)d;

a_{n}=\frac{a_{n-k}+a_{n+k}}{2} \quad (1\le k\le n-1);

S_{n}=\frac{a_{1}+a_{n}}{2}\cdot n=\frac{2a_{1}+d(n-1)}{2}\cdot n

Geometrik progressiya / Геометрическая прогрессия

b_{n}=b_{1}\cdot q^{n-1}; \quad b_{n}^{2}=b_{n-m}\cdot b_{n+m} \quad (1\le m\le n-1);

S_{n}=\frac{b_{1}(1-q^{n})}{1-q} \quad (|q|>1);

S_{n}=\frac{b_{1}}{1-q} \quad (|q|<1);

Logarifmning xossalari / Свойства логарифмов

log_{a}1=0; \quad log_{a}(x_{1}\cdot x_{2})=log_{a}|x_{1}|+log_{a}|x_{2}|;

log_{a}\frac{x_{1}}{x_{2}}=log_{a}|x_{1}|-log_{a}|x_{2}|; \quad log_{a}b=\frac{log_{c}b}{log_{c}a};

log_{a^{q}}x^{p}=\frac{p}{q}\cdot log_{a}x; \quad log_{a}b=\frac{1}{log_{b}a};

lg10^{n}=n; \quad lne^{n}=n;

Daraja va ildiz / Степень и корень

a^{n}\cdot a^{m}=a^{m+n}; \quad a^{n}:a^{m}=a^{m-n}; \quad (a^{m})^{n}=a^{m\cdot n};

(a\cdot b)^{n}=a^{n}\cdot b^{n}; \quad (\frac{a}{b})^{n}=\frac{a^{n}}{b^{n}}; \quad a^{-n}=\frac{1}{a^{n}};

(\frac{a^{n}}{b^{m}})^{-k}=(\frac{b^{m}}{a^{n}})^{k}; \quad (-a)^{2n}=a^{2n}; \quad (-a)^{2n+1}=-a^{2n+1};

\sqrt[n]{a^{k}}=a^{\frac{k}{n}}; \quad \sqrt[n]{a^{k}\cdot b^{m}}=\sqrt[n]{a^{k}}\cdot\sqrt[n]{b^{m}};

\sqrt[n]{\frac{a^{k}}{b^{m}}}=\frac{\sqrt[n]{a^{k}}}{\sqrt[n]{b^{m}}}; \quad (\sqrt[n]{a^{m}})^{k}=\sqrt[n]{a^{mk}}; \quad \sqrt[n]{a^{n+k}}=a\sqrt[n]{a^{k}};

a^{-\frac{k}{n}}=\frac{1}{\sqrt[n]{a^{k}}}; \quad \sqrt[n]{\sqrt[m]{a^{k}}}=\sqrt[nm]{a^{k}};

\sqrt[n]{a^{k}}\cdot\sqrt[m]{b^{p}}=\sqrt[nm]{a^{km}\cdot b^{pn}}; \quad \sqrt[n]{a^{n}}=|a| \quad (n=2k);

\sqrt[2n]{(a-b)^{2n}}=\begin{cases}a-b, & a\ge b\\ b-a, & b\ge a\end{cases}

Urinma va normal tenglamasi / Уравнение касательной и нормали

y=f(x_{0})+f^{\prime}(x_{0})(x-x_{0});

y=f(x_{0})-\frac{1}{f^{\prime}(x_{0})}(x-x_{0});

Hosilaga doir formulalar va xossalari / Таблица производных и свойства

(x^{a})^{\prime}=ax^{a-1}; \quad (a^{x})^{\prime}=a^{x}ln a; \quad (e^{x})^{\prime}=e^{x};

(log_{a}x)^{\prime}=\frac{1}{x ln a}; \quad (ln x)^{\prime}=\frac{1}{x}; \quad (sin x)^{\prime}=cos x;

(cos x)^{\prime}=-sin x; \quad (tg x)^{\prime}=\frac{1}{cos^{2}x}; \quad (ctg x)^{\prime}=-\frac{1}{sin^{2}x};

(u\pm v)^{\prime}=u^{\prime}\pm v^{\prime}; \quad (k\cdot u)^{\prime}=k\cdot u^{\prime};

(u\cdot v)^{\prime}=u^{\prime}\cdot v+u\cdot v^{\prime}; \quad (\frac{u}{v})^{\prime}=\frac{u^{\prime}\cdot v-u\cdot v^{\prime}}{v^{2}};

Integralga doir formulalar va xossalari / Таблица и свойства интегралов

\int x^{n}dx=\frac{x^{n+1}}{n+1}+C; \quad \int\frac{dx}{x}=ln|x|+C;

\int e^{x}dx=e^{x}+C; \quad \int a^{x}dx=\frac{a^{x}}{lna}+C;

\int sinx dx=-cosx+C; \quad \int cosx dx=sinx+C;

\int k\cdot f(x)dx=k\cdot\int f(x)dx;

\int(f(x)+g(x))dx=\int f(x)dx+\int g(x)dx;

\int_{a}^{b}f(x)dx=F(b)-F(a); \quad \int_{a}^{b}f(x)dx=-\int_{b}^{a}f(x)dx;

\int_{a}^{b}f(x)dx=\int_{a}^{c}f(x)dx+\int_{c}^{b}f(x)dx \quad (a\le c\le b);

O'rta arifmetik va o'rta geometrik / Среднее арифметическое и среднее геометрическое

A=\frac{a_{1}+a_{2}+...+a_{n}}{n}; \quad G=\sqrt[n]{a_{1}\cdot a_{2}\cdot...\cdot a_{n}}

Ba'zi trigonometrik formulalar / Основные формулы тригонометрии

Asosiy trigonometrik ayniyatlar / Основные тригонометрические свойства:

sin^{2}\alpha+cos^{2}\alpha=1; \quad tg\alpha=\frac{sin\alpha}{cos\alpha}; \quad ctg\alpha=\frac{cos\alpha}{sin\alpha};

tg^{2}\alpha+1=\frac{1}{cos^{2}\alpha}; \quad ctg^{2}\alpha+1=\frac{1}{sin^{2}\alpha};

cos(\alpha\pm\beta)=cos\alpha\cdot cos\beta\mp sin\alpha\cdot sin\beta;

sin(\alpha\pm\beta)=sin\alpha\cdot cos\beta\pm cos\alpha\cdot sin\beta;

tg(\alpha\pm\beta)=\frac{tg\alpha\pm tg\beta}{1\mp tg\alpha\cdot tg\beta}; \quad ctg(\alpha\pm\beta)=\frac{ctg\alpha\cdot ctg\beta\mp1}{ctg\alpha\pm ctg\beta};

sin\alpha+sin\beta=2sin\frac{\alpha+\beta}{2}cos\frac{\alpha-\beta}{2};

sin\alpha-sin\beta=2sin\frac{\alpha-\beta}{2}cos\frac{\alpha+\beta}{2};

cos\alpha+cos\beta=2cos\frac{\alpha+\beta}{2}cos\frac{\alpha-\beta}{2};

cos\alpha-cos\beta=-2sin\frac{\alpha+\beta}{2}sin\frac{\alpha-\beta}{2};

Trigonometrik funksiyaning ba'zi burchaklardagi qiymatlari / Значения тригонометрической функции под некоторыми углами

$\alpha$	0	$\frac{\pi}{6}$	$\frac{\pi}{4}$	$\frac{\pi}{3}$	$\frac{\pi}{2}$
$\sin\alpha$	0	$\frac{1}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{3}}{2}$	1
$\cos\alpha$	1	$\frac{\sqrt{3}}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{1}{2}$	0

To'g'ri burchakli uchburchak uchun formulalar / Формулы для прямоугольного треугольника

a^2 + b^2 = c^2;

a = c \cdot \sin\alpha

b = c \cdot \cos\alpha;

a = b \cdot \text{tg}\alpha

Ixtiyoriy uchburchak uchun formulalar / Формулы для произвольного треугольника

S = \frac{1}{2}ab\sin\gamma

S = \sqrt{p(p - a)(p - b)(p - c)}

p = \frac{1}{2}(a + b + c); \quad S = \frac{1}{2}h_c \cdot c

\frac{\sin\alpha}{a} = \frac{\sin\beta}{b} = \frac{\sin\gamma}{c}

a^2 = b^2 + c^2 - 2bc\cos\alpha

Uchburchak uchun formulalar (umumiy) / Формулы для треугольника (общие)

S=\frac{1}{2}ab sin\gamma; \quad S=\sqrt{p(p-a)(p-b)(p-c)};

p=\frac{1}{2}(a+b+c); \quad S=\frac{1}{2}h_{c}\cdot c;

\frac{a}{sin\alpha}=\frac{b}{sin\beta}=\frac{c}{sin\gamma}=2R; \quad a^{2}=b^{2}+c^{2}-2bc cos\alpha;

To'g'ri burchakli uchburchak / прямоугольный треугольник:

a^{2}+b^{2}=c^{2}; \quad a=c\cdot sin\alpha; \quad b=c\cdot cos\alpha; \quad a=b\cdot tg\alpha;

Uchburchakka ichki va tashqi chizilgan aylana radiuslarini hisoblash formulasi /
Формула вычисления радиусов окружности, вписанной внутрь и вне треугольника

r=\frac{2S}{a+b+c}; \quad R=\frac{abc}{4S};

To'rtburchakning yuzlari uchun formulalar / Формулы граней четырехугольника

Parallelogramm / параллелограмм:

S=a\cdot h_{a}; \quad S=a\cdot b\cdot sin\alpha;

Romb / ромб:

S=\frac{1}{2}\cdot d_{1}\cdot d_{2}; \quad S=a^{2}\cdot sin\alpha;

Trapetsiya / трапеция:

S=\frac{a+b}{2}\cdot h;

Aylana va doira Doiraviy sektor va segment yuzi / Круговой сектор и сегментная грань

l=2\pi R; \quad S=\pi R^{2};

S_{sektor}=\frac{\pi R^{2}}{360}\cdot\alpha; \quad S_{segment}=\frac{R^{2}}{2}(\alpha-sin\alpha);

Vektorlar / Векторы

|\vec{a}|=\sqrt{x^{2}+y^{2}+z^{2}}

vektorning uzunligi / длина вектора

\vec{a}\cdot\vec{b}=|\vec{a}|\cdot|\vec{b}|\cdot cos\varphi

skalyar ko'paytmasi / скалярное умножение

\vec{a}\cdot\vec{b}=x_{1}\cdot x_{2}+y_{1}\cdot y_{2}

vektorlarning skalyar ko'paytmasi / скалярное произведение векторов

\vec{a}\cdot\lambda=\vec{c}(x\cdot\lambda;y\cdot\lambda;z\cdot\lambda)

Stereometriya formulalari / Формулы стереометрии

Prizma / призма | Piramida / пирамида:

V=S\cdot H; \quad V=\frac{1}{3}S\cdot H;

Kesik piramida / усеченная пирамида:

V=\frac{1}{3}h(S_{1}+\sqrt{S_{1}\cdot S_{2}}+S_{2});

Silindr / цилиндр:

S_{yon}=2\pi RH; \quad V=\pi R^{2}H;

Konus / конус:

S_{yon}=\pi R l; \quad V=\frac{1}{3}\pi R^{2}H;

Kesik konus / усеченный конус:

V=\frac{1}{3}\pi h(R_{1}^{2}+R_{1}\cdot R_{2}+R_{2}^{2});

Shar / шар:

S=4\pi R^{2}; \quad V=\frac{4}{3}\pi R^{3};

Shar segmentining hajmi / объем шар сегмента:

V=\pi H^{2}(R-\frac{H}{3});

Shar segmentining sirtining yuzi / площадь поверхности шарового сегмента:

S_{sirt}=2\pi RH;

Agar

a \cdot b = 2^3 \cdot 3^5 \cdot 7^2

bo'lsa,

EKUK(a; b)

ning eng kichik qiymatini toping.

[200; 1000]

kesmada 2, 3, 5 va 7 sonlariga bo'lganda qoldiq 1 ga teng bo'ladigan natural sonlar nechta?

1 soatda Anvar 20 ta homashyo ishlab chiqaradi. Sardor esa 1 soatda 21 ta homashyo ishlab chiqaradi. Sardor 10 daqiqa oldin ishni tugatgan bo'lsa, jami nechta homashyo ishlab chiqarilgan?

Sotuvchi 2 xil mahsulotni 35000000 ga sotib 40% foyda qilgan. Agar 1-mahsulotdan 25%, 2-mahsulotdan 50% foyda ko'rgan bo'lsa, 2-mahsulotning narxini toping.

Hisoblang:

\frac{2^{98} + 1}{2^{49} + 2^{25} + 1}

Hisoblang:

\frac{1}{\sqrt{7 - \sqrt{24}}} - \frac{1}{\sqrt{7 + \sqrt{24}}}

Hisoblang:

\sqrt{2664^2 - 1776^2 - 888^2}

Arifmetik progressiyada

a_{98} = a_{99}

a_{2n-1} + 1 = a_{3n+1} - 2a_{n+1} + a_n

bo'lsa,

S_{100}

ni toping.

4x - x^2 = C_1

tenglamaning ildizlari

x_1

x_2

ga,

36x - x^2 = C_2

tenglamaning ildizlari

x_3

x_4

ga teng. Agar

x_1, x_2, x_3, x_4

sonlari geometrik progressiyani tashkil etsa,

\sqrt{C_1 \cdot C_2}

ning qiymatini toping.

10.

Agar

2025^3 - 2023^3 = a

bo'lsa,

\sqrt{\frac{a - 2}{6}}

ning qiymatini toping.

11.

Soddalashtiring:

\left(\frac{1}{\sqrt{x} - \sqrt{y}} - \frac{\left(\sqrt{y} + \sqrt{x}\right)^2}{x\sqrt{x} - y\sqrt{y}}\right) : \left(\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{y}}\right)^{-1}

12.

Hisoblang:

\cos 1125^\circ + \sin\frac{17\pi}{6}

13.

Tenglama

\left[-\frac{3\pi}{2}; \frac{\pi}{4}\right]

oraliqdagi ildizlari sonini toping.

6\sin^2 x - 2\sin 2x = 5

14.

Tengsizlikni yeching:

x^2 \cdot 3^x + 9 > 3^x + 9x^2

15.

Tengsizlikni yeching:

\log_{(x-2)}(x^2 - 4x + 3) < \log_{(x-2)} 1

16.

Tenglamani yeching:

|x^2 - 3| = 5

17.

Tenglamalar sistemasidan

\frac{x + y}{z}

ni toping:

\begin{cases} (x + y)(x + y + z) = 108 \\ (x + z)(x + y + z) = 120 \\ (y + z)(x + y + z) = 60 \end{cases}

18.

Tengsizlikning butun yechimlari yig'indisini (agar u bitta bo'lsa, shu ildizini) toping:

|x^2 - 5x + 2| \cdot \sqrt{10 - 3x - x^2} \le 0

19.

Tengsizlikning butun yechimlari yig'indisini toping.

\frac{2^{2x} - 3 \cdot 2^{2x-1} + 2}{x + 4} > 0

20.

Agar

f(x) = 3 + \frac{x}{1 + x}

bo'lsa,

f^{-1}(x)

ning qiymatini toping. (Bunda

f^{-1}(x)

—

f(x)

funksiyaning teskari funksiyasi).

21.

Aniq integralni hisoblang:

\int_0^{\frac{\pi}{4}} \frac{\sin^6 x}{\cos^8 x}\,dx

22.

f(x) = \sqrt{x + 2\sqrt{2x - 4}} - \sqrt{x - 2\sqrt{2x - 4}}

bo'lsa,

f'(6)

ning qiymatini toping.

23.

Kvadratga aylana ichki chizilgan. Kvadrat perimetrini aylana uzunligiga nisbatini toping.

24.

Agar

f(x)

toq funksiya va

f(x) - x^2 f(-x) = x^3 + 5x

bo'lsa,

f(-1)

ning qiymatini toping.

25.

ABC

uchburchak ichiga markazi

O

nuqtada bo'lgan aylana ichki chizilgan. Agar

\angle AOB = 150^\circ

AC = 13

BC = 8

bo'lsa,

ABC

uchburchakning yuzini toping.

26.

Ushbu rasmda

ABC

to'g'ri burchakli uchburchak tasvirlangan. Agar

\angle BAD = \angle ACB

AD = 10

AC = 15

bo'lsa,

ABD

uchburchak yuzini

ADC

uchburchak yuziga nisbatini toping.

27.

Ushbu rasmda

ABCD

DEFG

kvadratlar tasvirlangan. Agar

AD = 16

M

N

nuqtalar mos ravishda

GF

BC

tomonning o'rtalari bo'lsa,

ANM

uchburchakning yuzini toping.

28.

Ushbu rasmda

ABCDEFGH

muntazam sakkizburchak tasvirlangan bo'lib, uning

AD

BF

diagonallari

K

nuqtada kesishadi.

DEFK

to'rtburchak yuzini

ABK

uchburchak yuziga nisbati

\left(\frac{S_2}{S_1}\right)

ni toping.

29.

Qavariq to'rtburchakning uchlari

A(0; 0)

B(1; 2)

C(3; 3)

D(4; 0)

nuqtalarda yotadi.

DC

tomonida

E

nuqta shunday joylashga,

AE

kesma

ABCD

qavariq to'rtburchak yuzini teng ikkiga bo'ladi.

E

nuqtaning koordinatasini toping.

30.

Muntazam to'rtburchakli piramida apofemasi asos tekisligi bilan

45^\circ

burchak hosil qiladi. Agar yon sirti yuzi

144\sqrt{2}

ga teng bo'lsa, piramida hajmini toping.

31.

A = \{x \mid 2 \le x \le 4\}

B = \{x \mid 6 \le x \le 8\}

C = \{x \mid 3 \le x \le 7\}

D = \{x \mid 3 \le x \le 4\}

E = \{x \mid 6 \le x \le 7\}

to'plamlar berilgan.

D

E

to'plamlar birlashmasiga o'xshash to'plamni toping.

32.

a, b

c

raqamlar uchun

5 > a > b > c

tenglikni qanoatlantiruvchi nechta

\overline{abc}

uch xonali son tuzish mumkin?

Topshiriqlar (33-35) va javob variantlari (A-F) ni o'zaro moslashtiring.

33-35.

Ushbu rasmda diagonallari kesishgan nuqtasi

O

bo'lgan

ABCDA_1B_1C_1D_1

kub tasvirlangan.

M

N

nuqtalar mos ravishda

AD

AB

tomonlarning o'rtasida joylashgan.

Javob variantlari:

\frac{\sqrt{15}}{5}

\frac{\sqrt{15}}{4}

\frac{3}{5}

\frac{\sqrt{3}}{2}

\frac{4}{5}

\frac{\sqrt{10}}{5}

36.

Tenglamani yeching:

(x^3 + 3)^3 = 64 \cdot (4x - 3)

a) Tenglama nechta haqiqiy ildizga ega?

b) Tenglamaning haqiqiy ildizlari yig'indisini toping.

37.

Tenglamani yeching:

x^2 + 4x\cos(xy) + 4 = 0

. Bunda

-\pi \le xy \le \pi

a) Tenglamani qanoatlantiruvchi

(x; y)

juftliklar nechta?

x + y

ning eng kichik qiymatini toping.

38.

f(x)

funksiya uchun

2f(x) + 3f(-1) + f\left(\frac{1}{x}\right) = x

tenglik o'rinli.

f(1)

ning qiymatini toping.

b) Agar

f(x) = 1

tenglamaning ildizlari

x_1

x_2

bo'lsa,

\frac{1}{x_1^2} + \frac{1}{x_2^2}

ning qiymatini toping.

39.

y = f(x)

funksiya va

y = kx + l

urinma berilgan.

f'(1)

ni toping.

h(x) = (x^3 - 2x^2 + x + 3) \cdot f(x)

bo'lsa,

h'(1)

ni toping.

40.

Rasmda

y = f(x)

funksiya grafigi tasvirlangan. Rasmdagi ma'lumotlar asosida

\int_{-8}^{5}\left(|f'(x)| - f'(x)\right)dx

ni hisoblang.

\int_{-4}^{3}\left(f(x) + f'(x) \cdot x + f(x) \cdot f'(x)\right)dx

ni hisoblang.

41.

Ushbu rasmda ikkita uchi aylanada joylashgan

ABC

uchburchak tasvirlangan. Bunda

AB = 3

BD = 2

AD = 3

BDC

uchburchak yuzini toping.

b) Aylana radiusini toping.

42.

Ushbu rasmda

ABCD

kvadrat tasvirlangan.

ABC

uchburchak ichidan

E

nuqta shunday joylashganki, bunda

AE = \sqrt{3}

DE = 2\sqrt{3}

EC = 2\sqrt{5}

tengliklar o'rinli.

ABCD

kvadrat yuzini toping.

ACE

uchburchakning yuzini toping.

43.

Rasmda

ABCDEFGH

muntazam sakkizburchak tasvirlangan. Agar

HK = 12

\angle KHG = 60^\circ

ga teng bo'lsa,

BC

tomon uzunligini toping.

AKG

uchburchak yuzini toping.

44.

Muntazam uchburchakli kesik piramidaning ichiga shar ichki chizilgan. Asoslarining yuzlari

9\sqrt{3}

36\sqrt{3}

ga teng.

a) Kesik piramidaning yon sirtini toping.

b) Shar sirtining yuzini toping. (

\pi \approx 3

deb oling)

45.

Ushbu rasmda barcha qirralari 4 cm ga teng bo'lgan

ABCDE

muntazam to'rtburchakli piramida tasvirlangan.

AE

tomonning o'rtasi

F

nuqtada turgan chumoli piramidaning sirti bo'ylab

C

nuqtaga bormoqchi.

a) Chumoli

F

nuqtadan

C

nuqtagacha eng qisqa qancha masofa bosib o'tadi? (cm)

b) Agar chumoli har 2 daqiqada

\sqrt{7}

cm masofa bosib o'tsa,

F

dan

C

gacha qancha daqiqa vaqt sarflaydi?

Savol	A	B	C	D	E	F
33. $MON$ burchak sinusini toping.
34. $MD_1O$ burchak kosinusini toping.
35. $MCN$ burchak kosinusini toping.