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
$$\frac{x}{2} = 2 \pi n - \frac{\pi}{2}$$
$$\frac{x}{2} = 2 \pi n + \frac{3 \pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\frac{1}{2}$$
получим ответ:
$$x_{1} = 4 \pi n - \pi$$
$$x_{2} = 4 \pi n + 3 \pi$$

Быстрый ответ

x1 = -pi

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

x2 = 3*pi

$$x_{2} = 3 \pi$$

Сумма и произведение корней

сумма

0 - pi + 3*pi

$$\left(- \pi + 0\right) + 3 \pi$$

=

2*pi

$$2 \pi$$

произведение

1*-pi*3*pi

$$3 \pi 1 \left(- \pi\right)$$

=

     2
-3*pi 

$$- 3 \pi^{2}$$

Численный ответ

x1 = -3.14159244591793

x2 = -53.4070744460719

x3 = -91.1061879410652

x4 = 72.2566302523232

x5 = 47.1238897245433

x6 = -91.1061893000426

x7 = -78.5398160355522

x8 = -3.14159296369468

x9 = -3.1415920909332

x10 = 21.9911476515378

x11 = -91.1061866269766

x12 = 72.2566310277173

x13 = -65.9734464982309

x14 = -40.840702830856

x15 = -53.4070760410661

x16 = 34.5575182674959

x17 = -91.1061859213063

x18 = -15.7079640213661

x19 = 84.8230013528861

x20 = -3.14159363499305

x21 = -40.8407040589859

x22 = 72.2566319571987

x23 = 97.3893725976594

x24 = 72.2566318142828

x25 = -91.1061864056832

x26 = 47.1238883520716

x27 = 9.42477828111644

x28 = 34.5575190198289

x29 = -40.8407034751919

x30 = 9.4247774082407

x31 = -40.8407057343968

x32 = 9.42477785524033

x33 = 97.3893735581761

x34 = -28.2743336521146

x35 = 84.8230017459365

x36 = -65.9734457649054

x37 = -3.1415950208335

x38 = -15.7079641216365

x39 = 34.5575198674508

x40 = 34.5575201953822

x41 = -78.5398173635881

x42 = 97.3893732551872

x43 = 21.9911478139095

x44 = -53.4070752977589

x45 = 47.1238908281958

x46 = -40.8407049390955

x47 = 47.1238893765929

x48 = -65.9734448735059

x49 = -65.9734466347336

x50 = 47.123891242423

x51 = 97.3893712357817

x52 = -28.2743333728019

x53 = 59.6902594160982

x54 = 84.8230006713996

x55 = -40.840705514174

x56 = 84.8230022236836

x57 = 21.9911493543639

x58 = -53.4070755183111

x59 = -28.2743337045464

x60 = -28.2743329527591

x61 = -40.8407043325125

x62 = -103.672556618325

x63 = -103.672558275184

x64 = -3.14159162121992

x65 = -15.7079624977706

x66 = 34.5575202880375

x67 = 72.2566301889781

x68 = 59.6902613557236

x69 = 21.9911485852083

x70 = -65.9734467103803

x71 = -28.2743345506996

x72 = 47.123890256687

x73 = -91.10618728017

x74 = 9.42477894916069

x75 = 84.8230026783574

x76 = 59.6902608771019

x77 = -3.14159389871743

x78 = 59.6902606135717

x79 = -15.7079623299946

x80 = -28.2743348785101

x81 = -78.5398169064311

x82 = 21.9911494370191

x83 = -78.5398153571806

x84 = 59.6902597628977

x85 = 9.42477693583124

x86 = -53.407074099621

x87 = -15.7079632966168

x88 = 47.1238887891963

x89 = 34.5575187273286

x90 = 59.6902591286344

x91 = -78.5398163457967

x92 = 97.3893717230424

x93 = -65.9734449211945

График