sin(x/2)=1 (уравнение)

Найду корень уравнения: sin(x/2)=1

Вы ввели

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

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

Подробное решение

Дано уравнение
$$\sin{\left(\frac{x}{2} \right)} = 1$$
- это простейшее тригонометрическое ур-ние
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:
$$x_{1} = 4 \pi n + \pi$$
$$x_{2} = 4 \pi n + \pi$$

Сумма и произведение корней

сумма

0 + pi

$$0 + \pi$$

=

pi

$$\pi$$

произведение

1*pi

$$1 \pi$$

=

pi

$$\pi$$

Быстрый ответ

x1 = pi

$$x_{1} = \pi$$

Численный ответ

x1 = 103.672556563684

x2 = 3.14159163746103

x3 = -97.389371602892

x4 = -47.1238918185856

x5 = 3.14159420425446

x6 = -97.389373195247

x7 = -9.42477728929078

x8 = -59.6902596538675

x9 = -59.690260457841

x10 = 65.9734457530019

x11 = -72.2566320255231

x12 = -21.9911485864393

x13 = 15.707964515786

x14 = 65.9734465921985

x15 = -84.8229998635885

x16 = -59.6902612768606

x17 = 91.1061882841015

x18 = 78.5398161786998

x19 = -9.42477839608986

x20 = -47.1238887712007

x21 = 53.4070740857414

x22 = 53.4070749521362

x23 = 91.1061865344779

x24 = 78.539815851887

x25 = -34.5575192441112

x26 = -84.8230006270304

x27 = 91.1061859410303

x28 = 15.7079622686986

x29 = 65.9734447951365

x30 = 15.7079637526952

x31 = -9.4247756652542

x32 = 91.1061853899956

x33 = 91.1061874144797

x34 = 40.840705066392

x35 = -72.2566334561862

x36 = -34.5575197491116

x37 = 78.5398162375612

x38 = -34.5575188772018

x39 = 91.106187979742

x40 = 78.5398170241526

x41 = 53.4070754394033

x42 = 28.2743338651742

x43 = 16741.5472539237

x44 = 15.7079642015151

x45 = 15.7079626060796

x46 = -72.2566308637416

x47 = 15.7079632663563

x48 = -47.1238907880697

x49 = -47.1238901219454

x50 = -34.5575182039711

x51 = 3.14159131070869

x52 = 28.2743331152018

x53 = 53.40707409148

x54 = 78.5398173426089

x55 = 28.2743348137489

x56 = 78.5398154218754

x57 = -21.9911477831607

x58 = 28.2743346582797

x59 = -47.1238892482917

x60 = 40.8407056713041

x61 = -47.123889537864

x62 = 53.4070761022138

x63 = -97.3893724564835

x64 = -72.2566317074393

x65 = 65.973446491358

x66 = -9.42477888681821

x67 = -21.9911493421841

x68 = -84.8230020968984

x69 = 14944.5562553885

x70 = -72.2566301070981

x71 = -84.8230026657071

x72 = -21.9911477182159

x73 = -59.6902594740223

x74 = 40.8407041945824

x75 = -97.3893712473886

x76 = -84.8230012168657

x77 = 3.14159221873501

x78 = -21.9911494917557

x79 = 53.4070745656255

x80 = 3.14159309886503

x81 = -72.2566304993376

x82 = -9.42477695202933

x83 = -9.42477813898924

x84 = -34.5575202139462

x85 = 65.9734449700497

x86 = 40.8407035181637

x87 = -59.6902611573573

x88 = 28.2743330336433

x89 = 3.14159367655067

x90 = -84.8230027834212

x91 = 15.7079634545545

x92 = 40.840704648726

x93 = 40.8407055286336

График