sin((6/17)x)=1 (уравнение)

Найду корень уравнения: sin((6/17)x)=1

Вы ввели

   /6*x\    
sin|---| = 1
   \ 17/    

$$\sin{\left(\frac{6 x}{17} \right)} = 1$$

Подробное решение

Дано уравнение
$$\sin{\left(\frac{6 x}{17} \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$\frac{6 x}{17} = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$\frac{6 x}{17} = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Или
$$\frac{6 x}{17} = 2 \pi n + \frac{\pi}{2}$$
$$\frac{6 x}{17} = 2 \pi n + \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\frac{6}{17}$$
получим ответ:
$$x_{1} = \frac{17 \pi n}{3} + \frac{17 \pi}{12}$$
$$x_{2} = \frac{17 \pi n}{3} + \frac{17 \pi}{12}$$

Быстрый ответ

     17*pi
x1 = -----
       12 

$$x_{1} = \frac{17 \pi}{12}$$

Сумма и произведение корней

сумма

    17*pi
0 + -----
      12 

$$0 + \frac{17 \pi}{12}$$

=

17*pi
-----
  12 

$$\frac{17 \pi}{12}$$

произведение

  17*pi
1*-----
    12 

$$1 \cdot \frac{17 \pi}{12}$$

=

17*pi
-----
  12 

$$\frac{17 \pi}{12}$$

Численный ответ

x1 = -13.3517698220048

x2 = 93.4623812824027

x3 = -31.1541286006834

x4 = 22.2529490551172

x5 = -13.351767466583

x6 = -13.3517688849214

x7 = -48.9564842832067

x8 = 75.6600232847614

x9 = -48.9564859151522

x10 = 4.45058947585499

x11 = 4.45058861761562

x12 = -84.5612007988757

x13 = 4.45059081202566

x14 = -31.1541282577625

x15 = -31.1541304615335

x16 = -84.5612035382469

x17 = 40.0553067665637

x18 = -31.1541265665254

x19 = -66.7588452986075

x20 = 93.4623829052977

x21 = -31.1541258615439

x22 = -13.3517681120623

x23 = -102.363559576496

x24 = 93.4623801593672

x25 = -84.5611987756615

x26 = 93.4623808626993

x27 = -48.9564869568671

x28 = 40.0553049303586

x29 = -13.3517689800675

x30 = 22.2529470607695

x31 = 75.6600217435057

x32 = -66.7588424417155

x33 = -48.9564843808055

x34 = -66.7588451162719

x35 = 22.252950791952

x36 = -13.3517702323462

x37 = -66.7588416307338

x38 = 75.6600228260869

x39 = 4.45059033999208

x40 = 57.8576639564416

x41 = -84.561202830554

x42 = 22.2529493690197

x43 = 57.8576656791416

x44 = 57.8576633336415

x45 = -66.758843481984

x46 = -102.363560350198

x47 = 40.0553072358736

x48 = -84.561201141061

x49 = 75.6600217883675

x50 = 40.0553077658745

x51 = 93.462380087533

x52 = 57.8576661548791

x53 = -84.5612024925731

x54 = -84.561203622765

x55 = 75.6600245350859

x56 = 57.8576653759121

x57 = 75.6600234028696

x58 = -48.9564866893091

x59 = -13.3517689914846

x60 = 40.0553072497022

x61 = -84.5612019430096

x62 = 22.2529465343456

x63 = 57.8576648113083

x64 = -66.7588448652763

x65 = 4.45058814643374

x66 = -48.9564850232

x67 = 22.2529487893942

x68 = -13.351767445286

x69 = 4.45059096508528

x70 = -102.363559167799

x71 = 75.6600224083802

x72 = 93.4623850026228

x73 = 75.6600241188932

x74 = -66.7588427098434

x75 = 22.2529479607536

x76 = 40.0553052875581

x77 = 93.4623825548081

x78 = 4.4505890094409

x79 = -66.7588443738388

x80 = 22.2529471103659

x81 = 40.0553055071441

x82 = -31.154127454502

x83 = -31.1541257720463

x84 = 93.4623817494156

x85 = 57.857663518456

x86 = 40.0553062102502

x87 = -48.9564840984614

x88 = -48.9564875552163

x89 = -31.1541268035088

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