sin(x/2)-1=0 (уравнение)

Найду корень уравнения: sin(x/2)-1=0

Вы ввели

   /x\        
sin|-| - 1 = 0
   \2/        

$$\sin{\left(\frac{x}{2} \right)} - 1 = 0$$

Подробное решение

Дано уравнение
$$\sin{\left(\frac{x}{2} \right)} - 1 = 0$$
- это простейшее тригонометрическое ур-ние

Перенесём -1 в правую часть ур-ния

с изменением знака при -1

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

Быстрый ответ

x1 = pi

$$x_{1} = \pi$$

Сумма и произведение корней

сумма

0 + pi

$$0 + \pi$$

=

pi

$$\pi$$

произведение

1*pi

$$1 \pi$$

=

pi

$$\pi$$

Численный ответ

x1 = 40.8407055286336

x2 = -84.8230026657071

x3 = -97.389373195247

x4 = -21.9911477182159

x5 = -84.8230012168657

x6 = 78.5398170241526

x7 = 91.1061865344779

x8 = 53.4070749521362

x9 = -21.9911493421841

x10 = 15.7079642015151

x11 = -47.1238901219454

x12 = -59.690260457841

x13 = 53.4070761022138

x14 = 40.8407035181637

x15 = 91.1061853899956

x16 = 3.14159367655067

x17 = 65.9734447951365

x18 = -21.9911494917557

x19 = -9.42477813898924

x20 = -34.5575197491116

x21 = -47.1238887712007

x22 = -9.4247756652542

x23 = 15.7079634545545

x24 = -84.8230006270304

x25 = -59.6902594740223

x26 = 91.1061882841015

x27 = -84.8229998635885

x28 = 40.8407041945824

x29 = 3.14159420425446

x30 = 40.8407056713041

x31 = -34.5575192441112

x32 = 3.14159221873501

x33 = 40.840705066392

x34 = 14944.5562553885

x35 = -72.2566301070981

x36 = 15.7079637526952

x37 = 53.40707409148

x38 = -84.8230027834212

x39 = 16741.5472539237

x40 = 28.2743348137489

x41 = -72.2566308637416

x42 = -59.6902596538675

x43 = 65.9734465921985

x44 = 78.5398173426089

x45 = 28.2743346582797

x46 = -34.5575188772018

x47 = 3.14159309886503

x48 = 15.7079622686986

x49 = 3.14159163746103

x50 = 28.2743331152018

x51 = -9.42477839608986

x52 = 28.2743338651742

x53 = 15.7079632663563

x54 = -84.8230020968984

x55 = -47.1238918185856

x56 = 65.9734457530019

x57 = -9.42477888681821

x58 = -34.5575202139462

x59 = 53.4070754394033

x60 = -47.1238907880697

x61 = 15.707964515786

x62 = -59.6902611573573

x63 = 78.539815851887

x64 = -72.2566304993376

x65 = 53.4070740857414

x66 = 65.973446491358

x67 = 91.1061874144797

x68 = 53.4070745656255

x69 = -72.2566320255231

x70 = -72.2566334561862

x71 = -9.42477695202933

x72 = 78.5398162375612

x73 = 15.7079626060796

x74 = 91.1061859410303

x75 = 78.5398154218754

x76 = -9.42477728929078

x77 = -47.123889537864

x78 = 65.9734449700497

x79 = 3.14159131070869

x80 = 78.5398161786998

x81 = 28.2743330336433

x82 = -34.5575182039711

x83 = 40.840704648726

x84 = -72.2566317074393

x85 = -97.389371602892

x86 = -21.9911485864393

x87 = -59.6902612768606

x88 = 103.672556563684

x89 = 91.106187979742

x90 = -21.9911477831607

x91 = -97.3893724564835

x92 = -47.1238892482917

x93 = -97.3893712473886

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