cos(x/7)=-1 (уравнение)

Найду корень уравнения: cos(x/7)=-1

Вы ввели

   /x\     
cos|-| = -1
   \7/     

$$\cos{\left(\frac{x}{7} \right)} = -1$$

Подробное решение

Дано уравнение
$$\cos{\left(\frac{x}{7} \right)} = -1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$\frac{x}{7} = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$\frac{x}{7} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Или
$$\frac{x}{7} = \pi n + \pi$$
$$\frac{x}{7} = \pi n$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\frac{1}{7}$$
получим ответ:
$$x_{1} = 7 \pi n + 7 \pi$$
$$x_{2} = 7 \pi n$$

Быстрый ответ

x1 = 7*pi

$$x_{1} = 7 \pi$$

Сумма и произведение корней

сумма

0 + 7*pi

$$0 + 7 \pi$$

=

7*pi

$$7 \pi$$

произведение

1*7*pi

$$1 \cdot 7 \pi$$

=

7*pi

$$7 \pi$$

Численный ответ

x1 = 21.991151522556

x2 = 21.9911477418788

x3 = 1253.4954691642

x4 = 65.9734446694622

x5 = 109.955750118269

x6 = -21.9911450076955

x7 = 21.991151752945

x8 = -21.991152157574

x9 = -21.9911494163524

x10 = 65.9734486623417

x11 = 21.9911504105696

x12 = -65.9734474414272

x13 = -65.9734421561072

x14 = -21.9911409862258

x15 = -65.9734431513297

x16 = -109.955739897532

x17 = 65.9734475680066

x18 = -65.9734466793023

x19 = 21.991148585209

x20 = 109.955739381666

x21 = 65.9734449001142

x22 = 65.9734421405363

x23 = 21.9911397696265

x24 = -65.9734380239998

x25 = -65.9734493065658

x26 = 65.9734483175401

x27 = 65.9734426265841

x28 = 21.9911521406704

x29 = -109.955739339113

x30 = 65.9734422289926

x31 = 2836.85817471226

x32 = 21.9911454818007

x33 = -109.955739304565

x34 = -65.9734427573824

x35 = 21.9911450763433

x36 = 21.9911490333085

x37 = -65.9734457648986

x38 = 21.9911449914601

x39 = 21.9911468737264

x40 = -21.9911516731028

x41 = -21.9911520762816

x42 = -21.9911573388711

x43 = -65.9734425563067

x44 = -21.9911516565901

x45 = -21.9911480761133

x46 = 21.9911495547231

x47 = -65.9734439043292

x48 = 109.955739289654

x49 = 21.9911454849446

x50 = 65.9734426367208

x51 = -65.9734482102566

x52 = -21.9911450345957

x53 = -21.991151053773

x54 = -21.9911459950274

x55 = -21.9911502838542

x56 = 65.9734489075445

x57 = -65.973454436764

x58 = -21.9911456173525

x59 = -21.9911556709859

x60 = -65.9734487980189

x61 = -21.9911467468757

x62 = 65.9734492698185

x63 = -65.9734488279896

x64 = 65.9734492889902

x65 = 21.9911461027223

x66 = 65.9734440313146

x67 = 109.955739768327

x68 = 21.9911511612625

x69 = -109.955742296545

x70 = 65.9734432592293

x71 = -65.9734451860671

x72 = -21.9911485864385

x73 = 109.955741786578

x74 = 21.9911560498887

x75 = -65.9734465745794

x76 = -65.973449228882

x77 = 65.9734461421905

x78 = -21.9911495634843

x79 = 65.9734368901863

x80 = -21.9911454016721

x81 = 65.9734457530082

x82 = 21.9911475527726

x83 = -65.9734421868415

x84 = -109.955751525328

x85 = 65.9734467128769

x86 = 21.9911521176244

x87 = -65.9734447615984

x88 = 65.9734530846333

x89 = -21.9911476034353

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