cos (x/2)=-1 (уравнение)

Найду корень уравнения: cos (x/2)=-1

Вы ввели

   /x\     
cos|-| = -1
   \2/     

$$\cos{\left(\frac{x}{2} \right)} = -1$$

Подробное решение

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

Быстрый ответ

x1 = 2*pi

$$x_{1} = 2 \pi$$

Численный ответ

x1 = 18.8495549415754

x2 = -18.8495563601837

x3 = -43.982296295854

x4 = -43.9822979202134

x5 = -18.8495572113627

x6 = 43.9822979229286

x7 = -69.1150380827831

x8 = 69.115037955532

x9 = 31.415926404003

x10 = -69.1150393645777

x11 = 31.4159268602638

x12 = 56.5486668446775

x13 = 6.28318624191326

x14 = -31.4159274639505

x15 = 56.5486681672153

x16 = -43.9822971745293

x17 = -18.8495548993085

x18 = -81.6814097251289

x19 = 6.28318528419795

x20 = -56.5486667805662

x21 = -56.5486683277755

x22 = -31.4159267991785

x23 = 31.4159259869291

x24 = 18.8495569537229

x25 = 94.2477803922665

x26 = 43.9822980146158

x27 = -56.5486687887842

x28 = 69.1150368714384

x29 = 6.28318445599649

x30 = -6.28318480992034

x31 = 43.982297169474

x32 = -31.4159267183799

x33 = -18.8495554800568

x34 = -69.1150405916551

x35 = 18.8495561010751

x36 = 973.893720162307

x37 = -18.8495569383691

x38 = -69.115038701061

x39 = -56.5486677946696

x40 = -420.973417050673

x41 = 81.6814083413212

x42 = 31.4159255107699

x43 = 81.6814091930517

x44 = -94.2477802857943

x45 = 31.4159275256971

x46 = 69.1150397628024

x47 = -43.9822980632848

x48 = 56.5486684458067

x49 = -94.2477786842917

x50 = -31.4159258676764

x51 = 56.5486675992574

x52 = -81.6814090382823

x53 = -56.548667456373

x54 = 94.2477787666659

x55 = 6.28318454684724

x56 = -6.28318437561383

x57 = 69.115038835587

x58 = -31.4159269573538

x59 = 43.9822962232996

x60 = 18.8495554920234

x61 = -6.28318597231491

x62 = -94.2477805989545

x63 = 94.2477796093523

x64 = -94.2477790629797

x65 = -18.8495543136467

x66 = -69.1150378269834

x67 = -31.4159255258029

x68 = 69.1150373651011

x69 = 69.1150394039813

x70 = 56.548668769019

x71 = -69.115037346238

x72 = 18.8495564877336

x73 = -43.9822963521153

x74 = 56.5486672894687

x75 = 81.6814094388795

x76 = -81.68140804614

x77 = 81.6814079898679

x78 = 94.2477805288104

x79 = 43.9822963919738

x80 = 81.681409932803

x81 = 81.6814069775521

x82 = -81.6814082319334

x83 = -94.2477794433785

x84 = 18.8495556154405

x85 = -6.28318627375063

x86 = -6.28318512498487

x87 = -81.6814098544517

x88 = -6.28318500560576

x89 = 6.28318608026041

x90 = 94.2477788210844

x91 = -6.28318630492991

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