sin(cos(x))=0 (уравнение)

Найду корень уравнения: sin(cos(x))=0

Вы ввели

sin(cos(x)) = 0

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

Подробное решение

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

Быстрый ответ

     pi
x1 = --
     2 

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

     3*pi
x2 = ----
      2  

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

x3 = 2*pi - I*im(acos(pi))

$$x_{3} = 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\pi \right)}\right)}$$

x4 = I*im(acos(pi)) + re(acos(pi))

$$x_{4} = \operatorname{re}{\left(\operatorname{acos}{\left(\pi \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\pi \right)}\right)}$$

Численный ответ

x1 = -95.8185759344887

x2 = 58.1194640914112

x3 = 73.8274273593601

x4 = 51.8362787842316

x5 = 83.2522053201295

x6 = 42.4115008234622

x7 = -51.8362787842316

x8 = -1.5707963267949

x9 = -92.6769832808989

x10 = -70.6858347057703

x11 = 54.9778714378214

x12 = -58.1194640914112

x13 = 26.7035375555132

x14 = -10.9955742875643

x15 = 29.845130209103

x16 = -80.1106126665397

x17 = -29.845130209103

x18 = 92.6769832808989

x19 = 14.1371669411541

x20 = 23.5619449019235

x21 = -7.85398163397448

x22 = 89.5353906273091

x23 = -45.553093477052

x24 = 95.8185759344887

x25 = -64.4026493985908

x26 = 64.4026493985908

x27 = 39.2699081698724

x28 = 10.9955742875643

x29 = -76.9690200129499

x30 = -39.2699081698724

x31 = 36.1283155162826

x32 = -86.3937979737193

x33 = -89.5353906273091

x34 = -42.4115008234622

x35 = 20.4203522483337

x36 = -14.1371669411541

x37 = -98.9601685880785

x38 = 76.9690200129499

x39 = 32.9867228626928

x40 = -54.9778714378214

x41 = 48.6946861306418

x42 = -67.5442420521806

x43 = -158.650429006285

x44 = -48.6946861306418

x45 = 80.1106126665397

x46 = -17.2787595947439

x47 = 1.5707963267949

x48 = 4.71238898038469

x49 = -36.1283155162826

x50 = -83.2522053201295

x51 = 45.553093477052

x52 = -23.5619449019235

x53 = -26.7035375555132

x54 = -4.71238898038469

x55 = 61.261056745001

x56 = 67.5442420521806

x57 = 70.6858347057703

x58 = -20.4203522483337

x59 = -73.8274273593601

x60 = -61.261056745001

x61 = -32.9867228626928

x62 = 98.9601685880785

x63 = 7.85398163397448

x64 = 17.2787595947439

x65 = 86.3937979737193

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