sin(2x/3)=1 (уравнение)

Найду корень уравнения: sin(2x/3)=1

Вы ввели

   /2*x\    
sin|---| = 1
   \ 3 /    

$$\sin{\left(\frac{2 x}{3} \right)} = 1$$

Подробное решение

Дано уравнение
$$\sin{\left(\frac{2 x}{3} \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$\frac{2 x}{3} = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$\frac{2 x}{3} = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Или
$$\frac{2 x}{3} = 2 \pi n + \frac{\pi}{2}$$
$$\frac{2 x}{3} = 2 \pi n + \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\frac{2}{3}$$
получим ответ:
$$x_{1} = 3 \pi n + \frac{3 \pi}{4}$$
$$x_{2} = 3 \pi n + \frac{3 \pi}{4}$$

Быстрый ответ

     3*pi
x1 = ----
      4  

$$x_{1} = \frac{3 \pi}{4}$$

Сумма и произведение корней

сумма

    3*pi
0 + ----
     4  

$$0 + \frac{3 \pi}{4}$$

=

3*pi
----
 4  

$$\frac{3 \pi}{4}$$

произведение

  3*pi
1*----
   4  

$$1 \cdot \frac{3 \pi}{4}$$

=

3*pi
----
 4  

$$\frac{3 \pi}{4}$$

Численный ответ

x1 = 58.9048627329472

x2 = 40.0553056216555

x3 = -63.6172522698008

x4 = -25.9181392756155

x5 = -63.6172519949886

x6 = -44.7676957748932

x7 = 21.2057508212945

x8 = 68.3296394608903

x9 = -25.9181401090048

x10 = 68.3296388376665

x11 = 96.6039739066388

x12 = 96.6039747221533

x13 = 49.4800852541714

x14 = 21.2057499607944

x15 = -101.31636268836

x16 = 30.630528168767

x17 = 77.7544186264236

x18 = -7.06858295504315

x19 = -35.3429167447594

x20 = -35.3429172790171

x21 = 40.0553070819492

x22 = -35.3429175689968

x23 = -25.9181386473884

x24 = 11.7809726000477

x25 = 49.4800839951106

x26 = 77.7544189508403

x27 = -54.1924731393054

x28 = -54.1924739270596

x29 = -35.3429181180292

x30 = -7.06858296536089

x31 = -101.316362478446

x32 = 58.9048627799318

x33 = 87.1791955219656

x34 = 2.35619518095828

x35 = 11.7809730197568

x36 = 11.7809718056087

x37 = 2.35619328795888

x38 = 40.0553062102261

x39 = -63.6172513162396

x40 = -73.0420295457858

x41 = 30.6305283794495

x42 = 30.6305289887747

x43 = -16.4933616847636

x44 = 87.1791965574552

x45 = -73.0420286658174

x46 = 68.3296401258188

x47 = -7.06858380906536

x48 = -16.4933611509842

x49 = -44.7676949149706

x50 = 77.7544175384484

x51 = -3805.25410092568

x52 = 68.3296401641528

x53 = -73.0420286901429

x54 = -91.8915843769667

x55 = -82.4668063908855

x56 = -82.4668077263244

x57 = -82.4668068884062

x58 = 77.754418339056

x59 = 58.904861927746

x60 = -91.8915858394445

x61 = -54.1924725016962

x62 = -73.0420299109162

x63 = -25.9181398388922

x64 = 21.2057510978913

x65 = 49.4800845863293

x66 = -7.06858349260637

x67 = 96.6039733306763

x68 = 21.2057498140536

x69 = 49.48008374237

x70 = 87.1791968117183

x71 = 2.35619373280554

x72 = -91.891584572031

x73 = 11.7809732247378

x74 = -16.4933606685476

x75 = -44.7676946168873

x76 = 40.0553079674768

x77 = -101.31636294339

x78 = -82.4668073604005

x79 = 87.1791956965912

x80 = 68.329640912536

x81 = -7.06858419319028

x82 = 58.9048615252711

x83 = 30.6305276061146

x84 = -54.1924725755342

x85 = -63.6172505508106

x86 = 2.35619442367468

x87 = -16.4933619920463

x88 = 96.6039740313682

x89 = -44.7676958923483

x90 = 49.4800850532919

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