cos(x/6)=-1 (уравнение)

Найду корень уравнения: cos(x/6)=-1

Вы ввели

   /x\     
cos|-| = -1
   \6/     

$$\cos{\left(\frac{x}{6} \right)} = -1$$

Подробное решение

Дано уравнение
$$\cos{\left(\frac{x}{6} \right)} = -1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$\frac{x}{6} = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$\frac{x}{6} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Или
$$\frac{x}{6} = \pi n + \pi$$
$$\frac{x}{6} = \pi n$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\frac{1}{6}$$
получим ответ:
$$x_{1} = 6 \pi n + 6 \pi$$
$$x_{2} = 6 \pi n$$

Быстрый ответ

x1 = 6*pi

$$x_{1} = 6 \pi$$

Сумма и произведение корней

сумма

0 + 6*pi

$$0 + 6 \pi$$

=

6*pi

$$6 \pi$$

произведение

1*6*pi

$$1 \cdot 6 \pi$$

=

6*pi

$$6 \pi$$

Численный ответ

x1 = 56.548668684857

x2 = 56.5486708580155

x3 = -18.8495541133921

x4 = 18.8495539132593

x5 = -56.5486701996953

x6 = 94.2477796093523

x7 = -18.8495538018019

x8 = -94.2477766096957

x9 = 94.2477786626589

x10 = 56.5486691864073

x11 = -18.8495589807508

x12 = 18.8495497686594

x13 = 56.5486658681814

x14 = 94.2477778265357

x15 = -56.5486706326888

x16 = 18.8495573398767

x17 = -94.247780331416

x18 = -18.8495601039398

x19 = 94.247781315942

x20 = -56.5486656493118

x21 = -56.5486674527724

x22 = -94.2477794428164

x23 = 18.8495573862429

x24 = -18.8495563709794

x25 = -18.8495572570416

x26 = -18.849557670041

x27 = 94.2477771321735

x28 = 18.8495586964117

x29 = 18.8495532762155

x30 = -56.5486647444303

x31 = 94.2477799925393

x32 = -56.5486665537429

x33 = -56.548669107116

x34 = -94.2477811921558

x35 = 56.5486652015604

x36 = 56.5486654440189

x37 = 18.8495565121296

x38 = -18.8495531960788

x39 = 56.548669352492

x40 = -56.5486705573192

x41 = -18.849552856884

x42 = 18.8495588074837

x43 = 18.8495529137283

x44 = 56.5486675986864

x45 = 56.5486700885762

x46 = 56.5486601767443

x47 = -56.5486651159088

x48 = 56.5486684917252

x49 = -56.5486612770652

x50 = -56.5486702851951

x51 = -56.5486699852813

x52 = -56.5486708426813

x53 = 94.2477765333861

x54 = -94.2477772492532

x55 = -94.2477765483004

x56 = 94.2477804697546

x57 = -18.8495586435297

x58 = 18.8495590057275

x59 = -56.5486647289403

x60 = 18.8495528907655

x61 = -18.8495529582179

x62 = 56.5486705490094

x63 = 810.530904531238

x64 = 18.8495547141391

x65 = 18.8495538535501

x66 = 207.345114905769

x67 = 56.548664715657

x68 = -18.8495554691314

x69 = 18.8495581454845

x70 = 18.8495587178306

x71 = 18.8495556118876

x72 = -56.5486657530209

x73 = -94.2477808339716

x74 = 94.2477766595753

x75 = -94.2477785270414

x76 = -18.8495545825764

x77 = 94.2477770870066

x78 = -18.8495580379805

x79 = 18.8495543704497

x80 = 94.2477820272015

x81 = -94.2477770413102

x82 = 56.5486647710951

x83 = -56.5486692258817

x84 = -56.5486683519506

x85 = 56.5486666874419

x86 = -18.8495514206819

x87 = 56.548670625441

x88 = -94.2477777079179

x89 = -94.2477819283784

x90 = -18.8495588700492

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