sinx=2cosx (уравнение)

Найду корень уравнения: sinx=2cosx

Вы ввели

sin(x) = 2*cos(x)

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

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = 2 \cos{\left(x \right)}$$
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)

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

=

atan(2)

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

произведение

1*atan(2)

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

=

atan(2)

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

Численный ответ

x1 = 26.2398899465124

x2 = 70.2221870967695

x3 = 79.6469650575389

x4 = -5.1760365893855

x5 = 4.24874137138388

x6 = 19.9567046393328

x7 = 29.3814826001022

x8 = 54.5142238288206

x9 = -55.4415190468222

x10 = -14.6008145501549

x11 = -93.1406308898997

x12 = 76.5053724039491

x13 = -33.4503704716936

x14 = 35.6646679072818

x15 = 32.523075253692

x16 = 57.6558164824104

x17 = 7.39033402497368

x18 = -96.2822235434895

x19 = -71.1494823147711

x20 = 23.0982972929226

x21 = 38.8062605608716

x22 = 73.3637797503593

x23 = -39.7335557788732

x24 = -36.5919631252834

x25 = 67.0805944431797

x26 = -24.0255925109243

x27 = 92.2133356718981

x28 = -2.0344439357957

x29 = 85.9301503647185

x30 = 48.231038521641

x31 = 126.770854861386

x32 = 51.3726311752308

x33 = -99.4238161970793

x34 = -68.0078896611814

x35 = -61.7247043540018

x36 = -58.583111700412

x37 = -49.1583337396426

x38 = -42.875148432463

x39 = -77.4326676219507

x40 = -30.3087778181038

x41 = -52.2999263932324

x42 = 95.3549283254879

x43 = 45.0894458680512

x44 = 10.5319266785635

x45 = 117.346076900616

x46 = -17.7424072037447

x47 = -89.9990382363099

x48 = -11.4592218965651

x49 = -46.0167410860528

x50 = 1.10714871779409

x51 = 107.921298939847

x52 = 89.0717430183083

x53 = -8.31762924297529

x54 = 13.6735193321533

x55 = -20.8839998573345

x56 = -83.7158529291303

x57 = 82.7885577111287

x58 = -27.167185164514

x59 = 41.9478532144614

x60 = 98.4965209790777

x61 = 2813953.92130298

x62 = -86.8574455827201

x63 = 60.7974091360002

x64 = 16.8151119857431

x65 = 63.93900178959

x66 = -64.8662970075916

x67 = -74.2910749683609

x68 = -80.5742602755405

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