sin(pi*cos(x))=0 (уравнение)

Найду корень уравнения: sin(pi*cos(x))=0

Вы ввели

sin(pi*cos(x)) = 0

$$\sin{\left(\pi \cos{\left(x \right)} \right)} = 0$$

Подробное решение

Дано уравнение
$$\sin{\left(\pi \cos{\left(x \right)} \right)} = 0$$
преобразуем
$$\sin{\left(\pi \cos{\left(x \right)} \right)} - 1 = 0$$
$$\sin{\left(\pi \cos{\left(x \right)} \right)} - 1 = 0$$
Сделаем замену
$$w = \sin{\left(\pi \cos{\left(x \right)} \right)}$$
Переносим свободные слагаемые (без w)
из левой части в правую, получим:
$$w = 1$$
Получим ответ: w = 1
делаем обратную замену
$$\sin{\left(\pi \cos{\left(x \right)} \right)} = w$$
подставляем w:

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     pi
x2 = --
     2 

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

     3*pi
x3 = ----
      2  

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

x4 = 2*pi

$$x_{4} = 2 \pi$$

Сумма и произведение корней

сумма

        pi   3*pi       
0 + 0 + -- + ---- + 2*pi
        2     2         

$$\left(\left(\left(0 + 0\right) + \frac{\pi}{2}\right) + \frac{3 \pi}{2}\right) + 2 \pi$$

=

4*pi

$$4 \pi$$

произведение

    pi 3*pi     
1*0*--*----*2*pi
    2   2       

$$2 \pi \frac{3 \pi}{2} 1 \cdot 0 \frac{\pi}{2}$$

=

0

$$0$$

Численный ответ

x1 = -56.5486675305907

x2 = 72.2566310277178

x3 = 36.1283155162826

x4 = 78.5398161836578

x5 = -59.6902604577813

x6 = 50.26548244634

x7 = -9.42477813160234

x8 = 70.6858347057703

x9 = -81.6814090381988

x10 = -14.1371669411541

x11 = 40.8407042757388

x12 = -69.1150385830821

x13 = 4.71238898038469

x14 = 37.6991120249559

x15 = 94.2477796093523

x16 = 42.4115008234622

x17 = -95.8185759344887

x18 = 9.42477819093586

x19 = 97.3893724806003

x20 = -65.9734457649362

x21 = 28.2743334298614

x22 = -1.5707963267949

x23 = 53.4070753367092

x24 = -6.2831851325502

x25 = 47.1238904238015

x26 = 58.1194640914112

x27 = -3.14159286961502

x28 = 14.1371669411541

x29 = 65.9734457529714

x30 = -53.4070752888404

x31 = -87.9645943586312

x32 = -58.1194640914112

x33 = -86.3937979737193

x34 = -12.5663703825556

x35 = 87.9645943358868

x36 = 43.9822971694605

x37 = -94.247779571246

x38 = -37.6991118772499

x39 = -43.9822971745429

x40 = 86.3937979737193

x41 = 56.5486676047515

x42 = -7.85398163397448

x43 = 65.9734457227835

x44 = -31.4159267102565

x45 = 15.7079634462417

x46 = -50.2654822903597

x47 = 31.4159267640362

x48 = 34.5575190259044

x49 = 95.8185759344887

x50 = 6.28318528421316

x51 = -75.3982238673507

x52 = 81.6814091821425

x53 = -80.1106126665397

x54 = -45.553093477052

x55 = -89.5353906273091

x56 = 51.8362787842316

x57 = -15.7079632965907

x58 = -47.1238900126307

x59 = 73.8274273593601

x60 = 29.845130209103

x61 = 62.8318528491497

x62 = 21.9911485852049

x63 = 100.530964762621

x64 = 59.6902606035903

x65 = -97.3893724457839

x66 = -29.845130209103

x67 = -23.5619449019235

x68 = -78.5398161050827

x69 = -21.9911485864427

x70 = -91.1061871527076

x71 = -67.5442420521806

x72 = -94.2477794484607

x73 = 12.5663704471189

x74 = 64.4026493985908

x75 = -34.557518956407

x76 = 91.1061861181207

x77 = -72.2566308693743

x78 = -73.8274273593601

x79 = 84.8230014229889

x80 = -100.530964679861

x81 = -28.2743337114178

x82 = -51.8362787842316

x83 = 75.3982239089134

x84 = 80.1106126665397

x85 = 7.85398163397448

x86 = 20.4203522483337

x87 = -36.1283155162826

x88 = 28.2743338651819

x89 = -25.1327414414482

x90 = 18.8495557028003

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