cos(x/8)=-1 (уравнение)

Найду корень уравнения: cos(x/8)=-1

Вы ввели

   /x\     
cos|-| = -1
   \8/     

$$\cos{\left(\frac{x}{8} \right)} = -1$$

Подробное решение

Дано уравнение
$$\cos{\left(\frac{x}{8} \right)} = -1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$\frac{x}{8} = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$\frac{x}{8} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Или
$$\frac{x}{8} = \pi n + \pi$$
$$\frac{x}{8} = \pi n$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\frac{1}{8}$$
получим ответ:
$$x_{1} = 8 \pi n + 8 \pi$$
$$x_{2} = 8 \pi n$$

Быстрый ответ

x1 = 8*pi

$$x_{1} = 8 \pi$$

Сумма и произведение корней

сумма

0 + 8*pi

$$0 + 8 \pi$$

=

8*pi

$$8 \pi$$

произведение

1*8*pi

$$1 \cdot 8 \pi$$

=

8*pi

$$8 \pi$$

Численный ответ

x1 = -25.1327451472908

x2 = 75.3982257834497

x3 = -75.3982342130213

x4 = -75.3982220923533

x5 = 25.132744782648

x6 = 25.1327450884288

x7 = -25.1327440695057

x8 = -75.3982200084971

x9 = -25.1327387707274

x10 = -75.3982205617539

x11 = 75.398219917232

x12 = 25.1327434329117

x13 = -25.1327451509697

x14 = -75.3982147729872

x15 = -25.1327389193273

x16 = -25.132741546876

x17 = 75.3982278090201

x18 = 25.1327451995551

x19 = 75.3982240233119

x20 = 25.1327331519568

x21 = 75.3982195751768

x22 = -75.3982247954208

x23 = 75.3982276152739

x24 = 75.3982276147801

x25 = 75.398223473656

x26 = -25.1327371107759

x27 = 25.1327398844966

x28 = 75.3982231218883

x29 = -75.3982276655648

x30 = 75.3982196869411

x31 = -75.3982212733595

x32 = -25.1327381911181

x33 = -25.1327311352671

x34 = -75.3982270819601

x35 = 75.398224932574

x36 = 75.398221245716

x37 = 75.3982257481521

x38 = 25.1327425920046

x39 = -75.3982238780436

x40 = 25.1327488038586

x41 = 25.1327407868853

x42 = 25.1327453526376

x43 = -75.3982268444701

x44 = 3996.10585885824

x45 = -75.3982215497781

x46 = 25.1327416899384

x47 = -25.132742455938

x48 = 75.3982266543045

x49 = -25.13274418367

x50 = 25.1327372675432

x51 = -75.3982241201939

x52 = 25.1327402017133

x53 = -25.1327433081899

x54 = -25.132740644933

x55 = -25.1327397496108

x56 = 25.1327441769857

x57 = -25.1327372202265

x58 = 25.132743961536

x59 = -75.398226846245

x60 = -75.3982195817499

x61 = 25.1327390421078

x62 = -75.3982196447925

x63 = 25.1327423078305

x64 = -25.1327374522607

x65 = -25.1327446988415

x66 = 75.3982265426616

x67 = -25.1327376073143

x68 = 125.663714712834

x69 = 25.132737111976

x70 = -75.3982256568904

x71 = 25.1327385110608

x72 = 25.1327373761456

x73 = -75.3982277936869

x74 = 25.1327382958433

x75 = 75.3982200770073

x76 = -75.398226432539

x77 = 75.3982136179609

x78 = 125.663712290292

x79 = 75.3982271693146

x80 = -25.1327409725674

x81 = -125.66371506186

x82 = 276.460156260331

x83 = 75.398221394094

x84 = -75.398227557772

x85 = 75.3982222259613

x86 = -75.3982200007078

x87 = -25.1327432284627

x88 = -25.1327453441551

x89 = 75.3982206636104

x90 = -75.3982229807733

x91 = 25.1327376874375

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