cos0,5x=-1 (уравнение)

Найду корень уравнения: cos0,5x=-1

Вы ввели

cos(0.5*x) = -1

$$\cos{\left(0.5 x \right)} = -1$$

Подробное решение

Дано уравнение
$$\cos{\left(0.5 x \right)} = -1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$0.5 x = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$0.5 x = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Или
$$0.5 x = \pi n + \pi$$
$$0.5 x = \pi n$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$0.5$$
получим ответ:
$$x_{1} = 2 \pi n + 2 \pi$$
$$x_{2} = 2 \pi n$$

Быстрый ответ

x1 = 6.28318530717959

$$x_{1} = 6.28318530717959$$

Сумма и произведение корней

сумма

0 + 6.28318530717959

$$0 + 6.28318530717959$$

=

6.28318530717959

$$6.28318530717959$$

произведение

1*6.28318530717959

$$1 \cdot 6.28318530717959$$

=

6.28318530717959

$$6.28318530717959$$

Численный ответ

x1 = 69.1150394039813

x2 = 81.6814069775521

x3 = -43.9822979202134

x4 = -18.8495569383691

x5 = 69.115038835587

x6 = -6.28318627375063

x7 = -56.5486683277755

x8 = 94.2477803922665

x9 = 43.9822963919738

x10 = 43.9822979229286

x11 = -18.8495572113627

x12 = -81.6814090382823

x13 = 6.28318624191326

x14 = -81.6814097251289

x15 = -31.4159269573538

x16 = -69.1150405916551

x17 = -31.4159267991785

x18 = -18.8495563601837

x19 = -43.9822980632848

x20 = -43.982296295854

x21 = -94.2477786842917

x22 = 18.8495549415754

x23 = -81.68140804614

x24 = 31.415926404003

x25 = -94.2477790629797

x26 = 18.8495556154405

x27 = 94.2477805288104

x28 = -43.9822963521153

x29 = -69.115037346238

x30 = -18.8495554800568

x31 = 69.1150397628024

x32 = 56.5486684458067

x33 = -18.8495548993085

x34 = -56.548667456373

x35 = -81.6814098544517

x36 = 43.9822962232996

x37 = -31.4159255258029

x38 = -56.5486667805662

x39 = 69.1150373651011

x40 = -6.28318437561383

x41 = 6.28318608026041

x42 = 18.8495564877336

x43 = -6.28318480992034

x44 = 43.9822980146158

x45 = -6.28318630492991

x46 = -69.1150378269834

x47 = -94.2477794433785

x48 = -81.6814082319334

x49 = 6.28318454684724

x50 = -31.4159274639505

x51 = 18.8495561010751

x52 = -69.1150380827831

x53 = 69.115037955532

x54 = 31.4159268602638

x55 = 43.982297169474

x56 = 56.5486675992574

x57 = 31.4159275256971

x58 = 973.893720162307

x59 = -6.28318597231491

x60 = -69.1150393645777

x61 = 31.4159259869291

x62 = 6.28318445599649

x63 = -18.8495543136467

x64 = -69.115038701061

x65 = 31.4159255107699

x66 = 6.28318528419795

x67 = -56.5486677946696

x68 = -94.2477802857943

x69 = 18.8495554920234

x70 = 56.548668769019

x71 = 94.2477796093523

x72 = 81.6814094388795

x73 = 18.8495569537229

x74 = 81.6814083413212

x75 = 94.2477788210844

x76 = -6.28318512498487

x77 = 56.5486681672153

x78 = 94.2477787666659

x79 = 56.5486672894687

x80 = 69.1150368714384

x81 = -43.9822971745293

x82 = 81.6814091930517

x83 = -31.4159267183799

x84 = -94.2477805989545

x85 = -420.973417050673

x86 = -31.4159258676764

x87 = 81.681409932803

x88 = 81.6814079898679

x89 = -6.28318500560576

x90 = 56.5486668446775

x91 = -56.5486687887842

График