sin(x/3)=1 (уравнение)

Найду корень уравнения: sin(x/3)=1

Вы ввели

   /x\    
sin|-| = 1
   \3/    

$$\sin{\left(\frac{x}{3} \right)} = 1$$

Подробное решение

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

Быстрый ответ

     3*pi
x1 = ----
      2  

$$x_{1} = \frac{3 \pi}{2}$$

Сумма и произведение корней

сумма

    3*pi
0 + ----
     2  

$$0 + \frac{3 \pi}{2}$$

=

3*pi
----
 2  

$$\frac{3 \pi}{2}$$

произведение

  3*pi
1*----
   2  

$$1 \cdot \frac{3 \pi}{2}$$

=

3*pi
----
 2  

$$\frac{3 \pi}{2}$$

Численный ответ

x1 = -127.234505848294

x2 = -32.9867232461325

x3 = -89.5353891908119

x4 = 42.4115022428113

x5 = -70.685834288633

x6 = -70.6858362309458

x7 = 80.1106135539297

x8 = 98.9601682288619

x9 = 23.5619466932833

x10 = 23.5619435650347

x11 = -70.685833157528

x12 = -70.685834331807

x13 = -89.5353907511938

x14 = 42.4114998547396

x15 = 23.5619451602171

x16 = 23.5619434127797

x17 = 98.9601670470878

x18 = 4.71239032744758

x19 = 80.1106131348724

x20 = -14.1371683493325

x21 = -32.9867240407822

x22 = 80.1106139543144

x23 = 80.1106141414446

x24 = -14.1371632785063

x25 = 4.71239047793188

x26 = -51.8362786892049

x27 = -32.9867221902905

x28 = -51.836280250587

x29 = -51.8362773184302

x30 = -32.9867213252475

x31 = 42.4114972812005

x32 = 4.71238873614443

x33 = 61.2610571768274

x34 = -89.5353916821637

x35 = -32.9867244036077

x36 = 61.2610571432374

x37 = 61.2610554909574

x38 = -70.6858359752153

x39 = 117.80972686857

x40 = 42.4114997223281

x41 = 2681.3493318713

x42 = -1465.5529710851

x43 = 61.2610562502557

x44 = 61.2610570541192

x45 = -89.5353938509755

x46 = 4.71238744831877

x47 = 80.1106118137324

x48 = -70.6858352240085

x49 = -14.1371658195785

x50 = 98.9601682192268

x51 = -14.1371676938022

x52 = 23.5619442758647

x53 = -89.5353932769431

x54 = -32.9867232128077

x55 = 61.2610579347666

x56 = -89.5353892213239

x57 = 23.5619459918487

x58 = 4.7123879028989

x59 = -14.1371668364463

x60 = 23.5619457138128

x61 = -70.6858335329831

x62 = 80.1106113644907

x63 = 4.71238962102704

x64 = 61.2610582931613

x65 = 42.4115015902858

x66 = -51.8362779176776

x67 = -89.5353916157766

x68 = -89.535392136822

x69 = 98.9601691211123

x70 = 42.411499320376

x71 = 42.4115007269796

x72 = -70.6858340827787

x73 = 4.71238820064707

x74 = -51.836277468404

x75 = 61.2610552150039

x76 = 98.9601674271064

x77 = 80.1106112094214

x78 = -32.9867215976396

x79 = 42.41150224098

x80 = -32.9867223531263

x81 = -51.836279657976

x82 = 4.71238732643494

x83 = -14.1371659592965

x84 = -89.535389882372

x85 = -32.9867231189461

x86 = -51.8362800573105

x87 = -14.1371654300911

x88 = -14.1371683499323

x89 = 23.5619464414432

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