ctg(x)=1/2 (уравнение)

Найду корень уравнения: ctg(x)=1/2

Вы ввели

cot(x) = 1/2

$$\cot{\left(x \right)} = \frac{1}{2}$$

Подробное решение

Дано уравнение
$$\cot{\left(x \right)} = \frac{1}{2}$$
преобразуем
$$\cot{\left(x \right)} - \frac{1}{2} = 0$$
$$\cot{\left(x \right)} - \frac{1}{2} = 0$$
Сделаем замену
$$w = \cot{\left(x \right)}$$
Переносим свободные слагаемые (без w)
из левой части в правую, получим:
$$w = \frac{1}{2}$$
Получим ответ: w = 1/2
делаем обратную замену
$$\cot{\left(x \right)} = w$$
подставляем w:

Быстрый ответ

x1 = acot(1/2)

$$x_{1} = \operatorname{acot}{\left(\frac{1}{2} \right)}$$

Сумма и произведение корней

сумма

0 + acot(1/2)

$$0 + \operatorname{acot}{\left(\frac{1}{2} \right)}$$

=

acot(1/2)

$$\operatorname{acot}{\left(\frac{1}{2} \right)}$$

произведение

1*acot(1/2)

$$1 \operatorname{acot}{\left(\frac{1}{2} \right)}$$

=

acot(1/2)

$$\operatorname{acot}{\left(\frac{1}{2} \right)}$$

Численный ответ

x1 = -49.1583337396426

x2 = -36.5919631252834

x3 = 41.9478532144614

x4 = 76.5053724039491

x5 = -68.0078896611814

x6 = 16.8151119857431

x7 = -93.1406308898997

x8 = 85.9301503647185

x9 = 29.3814826001022

x10 = -27.167185164514

x11 = 45.0894458680512

x12 = 23.0982972929226

x13 = -17.7424072037447

x14 = 92.2133356718981

x15 = -42.875148432463

x16 = 63.93900178959

x17 = 57.6558164824104

x18 = -86.8574455827201

x19 = 35.6646679072818

x20 = -83.7158529291303

x21 = -77.4326676219507

x22 = 32.523075253692

x23 = -55.4415190468222

x24 = -8.31762924297529

x25 = -39.7335557788732

x26 = 73.3637797503593

x27 = 26.2398899465124

x28 = 13.6735193321533

x29 = 95.3549283254879

x30 = -96.2822235434895

x31 = -52.2999263932324

x32 = -24.0255925109243

x33 = 10.5319266785635

x34 = 60.7974091360002

x35 = -64.8662970075916

x36 = -30.3087778181038

x37 = 82.7885577111287

x38 = 89.0717430183083

x39 = -74.2910749683609

x40 = -11.4592218965651

x41 = -99.4238161970793

x42 = 54.5142238288206

x43 = -71.1494823147711

x44 = -89.9990382363099

x45 = 19.9567046393328

x46 = 67.0805944431797

x47 = 38.8062605608716

x48 = -20.8839998573345

x49 = 51.3726311752308

x50 = 7.39033402497368

x51 = 70.2221870967695

x52 = 1.10714871779409

x53 = -33.4503704716936

x54 = -5.1760365893855

x55 = -80.5742602755405

x56 = 98.4965209790777

x57 = -61.7247043540018

x58 = -2.0344439357957

x59 = -58.583111700412

x60 = 48.231038521641

x61 = 4.24874137138388

x62 = -14.6008145501549

x63 = 79.6469650575389

x64 = -46.0167410860528

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