cos(x/5)=-1 (уравнение)

Найду корень уравнения: cos(x/5)=-1

Вы ввели

   /x\     
cos|-| = -1
   \5/     

$$\cos{\left(\frac{x}{5} \right)} = -1$$

Подробное решение

Дано уравнение
$$\cos{\left(\frac{x}{5} \right)} = -1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$\frac{x}{5} = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$\frac{x}{5} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Или
$$\frac{x}{5} = \pi n + \pi$$
$$\frac{x}{5} = \pi n$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\frac{1}{5}$$
получим ответ:
$$x_{1} = 5 \pi n + 5 \pi$$
$$x_{2} = 5 \pi n$$

Быстрый ответ

x1 = 5*pi

$$x_{1} = 5 \pi$$

Сумма и произведение корней

сумма

0 + 5*pi

$$0 + 5 \pi$$

=

5*pi

$$5 \pi$$

произведение

1*5*pi

$$1 \cdot 5 \pi$$

=

5*pi

$$5 \pi$$

Численный ответ

x1 = -78.5398151446878

x2 = 47.1238893672005

x3 = 204.203522241035

x4 = 15.7079609259173

x5 = 47.1238873084304

x6 = 47.1238911368643

x7 = 78.5398139484401

x8 = -109.955745597958

x9 = 15.7079651530831

x10 = -47.123891755735

x11 = -47.1238845327779

x12 = 78.5398186830988

x13 = 78.539819441708

x14 = 47.1238902678764

x15 = -15.707965329034

x16 = -15.707963787485

x17 = 15.7079651296196

x18 = 78.5398152747855

x19 = 78.5398170682907

x20 = 15.707961729282

x21 = -15.7079642265323

x22 = 15.707962566483

x23 = 78.5398189021442

x24 = -78.5398138890222

x25 = -15.7079606929945

x26 = -141.371669109372

x27 = -47.1238923366349

x28 = 15.7079656734751

x29 = 78.5398137772168

x30 = 1523.672431799

x31 = 109.955740633841

x32 = 109.955743388045

x33 = 47.123888495739

x34 = 78.5398144533592

x35 = 47.1238918530452

x36 = -109.955740761569

x37 = -78.5398143960206

x38 = 78.5398161781999

x39 = -47.1238892266369

x40 = 15.7079610707134

x41 = 47.1238873132795

x42 = -15.7079609905632

x43 = -47.1238913784282

x44 = 47.1238834902891

x45 = -78.5398170658543

x46 = 15.7079600690302

x47 = -78.5398188712212

x48 = 47.1238923027174

x49 = -78.5398210333058

x50 = -47.1238910102026

x51 = 15.7079643589024

x52 = -47.1238883718742

x53 = -47.1238872711186

x54 = -15.7079656074579

x55 = 47.1238961171027

x56 = -15.7079632966218

x57 = 78.5398144993885

x58 = 47.123892306231

x59 = -15.7079616129238

x60 = 78.539818554401

x61 = -15.7079610256452

x62 = 47.123891073275

x63 = -78.5398160322833

x64 = -78.5398146753102

x65 = -78.5398184687978

x66 = 15.7079658362819

x67 = -15.7079614567185

x68 = -15.7079624295751

x69 = -15.707965838961

x70 = -78.5398137921376

x71 = 15.7079607148849

x72 = -47.1238889196755

x73 = -78.5398187594684

x74 = -47.1238873586036

x75 = 15.7079634553212

x76 = 78.5398179019981

x77 = 78.5398165209218

x78 = 47.1238885314361

x79 = 47.1238877741124

x80 = -47.1238922564323

x81 = -78.5398177822968

x82 = 15.7079601534269

x83 = -109.955744308027

x84 = -47.1238876815792

x85 = 15.7079630812848

x86 = -47.1238901257198

x87 = -78.5398169297615

x88 = -15.7079650220913

x89 = 15.7079647632944

x90 = 78.5398220572023

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