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)

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

=

-acot(1/2)

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

произведение

1*-acot(1/2)

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

=

-acot(1/2)

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

Численный ответ

x1 = -98.4965209790777

x2 = 27.167185164514

x3 = 36.5919631252834

x4 = 93.1406308898997

x5 = -32.523075253692

x6 = 8.31762924297529

x7 = -79.6469650575389

x8 = 61.7247043540018

x9 = 99.4238161970793

x10 = -60.7974091360002

x11 = 30.3087778181038

x12 = 86.8574455827201

x13 = 83.7158529291303

x14 = -45.0894458680512

x15 = -63.93900178959

x16 = 17.7424072037447

x17 = 74.2910749683609

x18 = 55.4415190468222

x19 = -29.3814826001022

x20 = 96.2822235434895

x21 = -85.9301503647185

x22 = 20.8839998573345

x23 = -26.2398899465124

x24 = 49.1583337396426

x25 = -4.24874137138388

x26 = -38.8062605608716

x27 = 33.4503704716936

x28 = 58.583111700412

x29 = -95.3549283254879

x30 = -70.2221870967695

x31 = -89.0717430183083

x32 = 46.0167410860528

x33 = 2.0344439357957

x34 = -76.5053724039491

x35 = -51.3726311752308

x36 = -41.9478532144614

x37 = -35.6646679072818

x38 = 5.1760365893855

x39 = 52.2999263932324

x40 = -1.10714871779409

x41 = -13.6735193321533

x42 = -10.5319266785635

x43 = -82.7885577111287

x44 = 71.1494823147711

x45 = 77.4326676219507

x46 = 68.0078896611814

x47 = 11.4592218965651

x48 = -48.231038521641

x49 = 80.5742602755405

x50 = 42.875148432463

x51 = 39.7335557788732

x52 = -92.2133356718981

x53 = -67.0805944431797

x54 = -7.39033402497368

x55 = 64.8662970075916

x56 = 14.6008145501549

x57 = -19.9567046393328

x58 = 24.0255925109243

x59 = -57.6558164824104

x60 = -54.5142238288206

x61 = -16.8151119857431

x62 = -23.0982972929226

x63 = 89.9990382363099

x64 = -73.3637797503593

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