sin(x)+2cos(x)=0 (уравнение)

Найду корень уравнения: sin(x)+2cos(x)=0

Вы ввели

sin(x) + 2*cos(x) = 0

$$\sin{\left(x \right)} + 2 \cos{\left(x \right)} = 0$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} + 2 \cos{\left(x \right)} = 0$$
преобразуем:
$$\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} = -2$$
или
$$\tan{\left(x \right)} = -2$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{atan}{\left(2 \right)}$$
Или
$$x = \pi n + \operatorname{atan}{\left(2 \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -atan(2)

$$x_{1} = - \operatorname{atan}{\left(2 \right)}$$

Сумма и произведение корней

сумма

0 - atan(2)

$$- \operatorname{atan}{\left(2 \right)} + 0$$

=

-atan(2)

$$- \operatorname{atan}{\left(2 \right)}$$

произведение

1*-atan(2)

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

=

-atan(2)

$$- \operatorname{atan}{\left(2 \right)}$$

Численный ответ

x1 = -98.4965209790777

x2 = 27.167185164514

x3 = 36.5919631252834

x4 = -243.009783044208

x5 = 93.1406308898997

x6 = -32.523075253692

x7 = 8.31762924297529

x8 = -79.6469650575389

x9 = 61.7247043540018

x10 = 99.4238161970793

x11 = -60.7974091360002

x12 = 30.3087778181038

x13 = 86.8574455827201

x14 = 83.7158529291303

x15 = -45.0894458680512

x16 = -63.93900178959

x17 = -104.779706286257

x18 = 17.7424072037447

x19 = 74.2910749683609

x20 = 55.4415190468222

x21 = -29.3814826001022

x22 = 96.2822235434895

x23 = -85.9301503647185

x24 = 20.8839998573345

x25 = -26.2398899465124

x26 = 49.1583337396426

x27 = -4.24874137138388

x28 = -38.8062605608716

x29 = 33.4503704716936

x30 = 58.583111700412

x31 = -95.3549283254879

x32 = -70.2221870967695

x33 = -89.0717430183083

x34 = 46.0167410860528

x35 = 2.0344439357957

x36 = -76.5053724039491

x37 = -51.3726311752308

x38 = -41.9478532144614

x39 = -35.6646679072818

x40 = 5.1760365893855

x41 = 52.2999263932324

x42 = -1.10714871779409

x43 = -13.6735193321533

x44 = -10.5319266785635

x45 = -82.7885577111287

x46 = 71.1494823147711

x47 = 77.4326676219507

x48 = 68.0078896611814

x49 = 11.4592218965651

x50 = -48.231038521641

x51 = 80.5742602755405

x52 = 42.875148432463

x53 = 39.7335557788732

x54 = -92.2133356718981

x55 = -67.0805944431797

x56 = -7.39033402497368

x57 = 64.8662970075916

x58 = 14.6008145501549

x59 = -19.9567046393328

x60 = 24.0255925109243

x61 = -57.6558164824104

x62 = -54.5142238288206

x63 = -16.8151119857431

x64 = -23.0982972929226

x65 = 89.9990382363099

x66 = -73.3637797503593

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