sin(x/8)=1 (уравнение)

Найду корень уравнения: sin(x/8)=1

Вы ввели

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

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

Подробное решение

Дано уравнение
$$\sin{\left(\frac{x}{8} \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$\frac{x}{8} = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$\frac{x}{8} = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Или
$$\frac{x}{8} = 2 \pi n + \frac{\pi}{2}$$
$$\frac{x}{8} = 2 \pi n + \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\frac{1}{8}$$
получим ответ:
$$x_{1} = 16 \pi n + 4 \pi$$
$$x_{2} = 16 \pi n + 4 \pi$$

Быстрый ответ

x1 = 4*pi

$$x_{1} = 4 \pi$$

Сумма и произведение корней

сумма

0 + 4*pi

$$0 + 4 \pi$$

=

4*pi

$$4 \pi$$

произведение

1*4*pi

$$1 \cdot 4 \pi$$

=

4*pi

$$4 \pi$$

Численный ответ

x1 = -37.6991101207542

x2 = 12.5663730408046

x3 = -37.6991151969919

x4 = 113.097331412267

x5 = -37.6991101392263

x6 = 263.893784059973

x7 = 62.831850087879

x8 = 12.5663665083573

x9 = -37.6991077639261

x10 = 62.831855395083

x11 = 12.5663683201763

x12 = -87.9645933384073

x13 = 12.5663700970129

x14 = -37.6991128176

x15 = -37.699114479795

x16 = 12.5663713358946

x17 = -87.9645924661837

x18 = 12.5663743080805

x19 = 12.5663695208921

x20 = 62.8318567019423

x21 = -87.9645902531782

x22 = -37.6991110008632

x23 = 12.5663704397157

x24 = -37.6991186561388

x25 = 12.566374277561

x26 = 62.8318518602537

x27 = -87.9645904905769

x28 = 62.8318509287894

x29 = -87.9645916735435

x30 = 62.8318571883823

x31 = 62.831849141227

x32 = 12.5663678807347

x33 = 62.8318502434668

x34 = 62.8318561211209

x35 = -87.9645960343522

x36 = 12.5663672286976

x37 = -37.6991118772992

x38 = 12.5663667493227

x39 = 12.5663746597308

x40 = -37.6991077705609

x41 = 62.8318489570416

x42 = -87.9645980582877

x43 = -37.6991165776898

x44 = -37.6991136887584

x45 = 12.5663722233672

x46 = 12.5663686582411

x47 = -37.6991151509896

x48 = 62.8318570849532

x49 = 62.831853228777

x50 = -37.6991086234953

x51 = 62.8318491592384

x52 = -87.9645930509108

x53 = -37.6991049184923

x54 = -37.6991158736745

x55 = 12.5663672838155

x56 = -37.699108089375

x57 = -37.6991156564598

x58 = 113.097344057965

x59 = -87.9645909998932

x60 = 62.8318536718483

x61 = 62.8318496114042

x62 = -37.6991082987741

x63 = 62.8318527702744

x64 = 62.8318510067354

x65 = 62.8318545662664

x66 = -87.9645975277768

x67 = -87.9645968382207

x68 = 12.5663666282045

x69 = 113.097331666594

x70 = -87.9645943585647

x71 = -37.6991129279702

x72 = -87.9646006577684

x73 = -87.964598370976

x74 = -87.9645951552855

x75 = -37.6991093153727

x76 = 12.566379304553

x77 = -87.9645902062015

x78 = 62.8318630948853

x79 = 12.5663674312132

x80 = 62.8318568360164

x81 = -37.6991159341943

x82 = -188.495559284869

x83 = 113.097336489978

x84 = 12.5663737501393

x85 = 12.5663747163559

x86 = 62.8318554897764

x87 = 113.097332777765

x88 = 12.5663727038475

x89 = -87.96459089549

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