sin(cosx)=0 (уравнение)

Найду корень уравнения: sin(cosx)=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))

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

Сумма и произведение корней

сумма

    pi   3*pi                                                        
0 + -- + ---- + 2*pi - I*im(acos(pi)) + I*im(acos(pi)) + re(acos(pi))
    2     2                                                          

$$\left(\left(\left(0 + \frac{\pi}{2}\right) + \frac{3 \pi}{2}\right) + \left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\pi \right)}\right)}\right)\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(\pi \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\pi \right)}\right)}\right)$$

=

4*pi + re(acos(pi))

$$\operatorname{re}{\left(\operatorname{acos}{\left(\pi \right)}\right)} + 4 \pi$$

произведение

  pi 3*pi                                                        
1*--*----*(2*pi - I*im(acos(pi)))*(I*im(acos(pi)) + re(acos(pi)))
  2   2                                                          

$$\frac{3 \pi}{2} \cdot 1 \frac{\pi}{2} \cdot \left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\pi \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\pi \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\pi \right)}\right)}\right)$$

=

    2                                                        
3*pi *(2*pi - I*im(acos(pi)))*(I*im(acos(pi)) + re(acos(pi)))
-------------------------------------------------------------
                              4                              

$$\frac{3 \pi^{2} \cdot \left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\pi \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\pi \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\pi \right)}\right)}\right)}{4}$$

Численный ответ

x1 = 64.4026493985908

x2 = -42.4115008234622

x3 = 54.9778714378214

x4 = 70.6858347057703

x5 = 39.2699081698724

x6 = -23.5619449019235

x7 = 76.9690200129499

x8 = 73.8274273593601

x9 = 95.8185759344887

x10 = -83.2522053201295

x11 = 67.5442420521806

x12 = 1.5707963267949

x13 = -45.553093477052

x14 = 98.9601685880785

x15 = 32.9867228626928

x16 = -54.9778714378214

x17 = 89.5353906273091

x18 = -20.4203522483337

x19 = 61.261056745001

x20 = -7.85398163397448

x21 = 86.3937979737193

x22 = -10.9955742875643

x23 = 14.1371669411541

x24 = -80.1106126665397

x25 = -64.4026493985908

x26 = -73.8274273593601

x27 = 26.7035375555132

x28 = -26.7035375555132

x29 = -14.1371669411541

x30 = 7.85398163397448

x31 = -92.6769832808989

x32 = 29.845130209103

x33 = -67.5442420521806

x34 = 58.1194640914112

x35 = -48.6946861306418

x36 = -76.9690200129499

x37 = -61.261056745001

x38 = -29.845130209103

x39 = 17.2787595947439

x40 = 48.6946861306418

x41 = 45.553093477052

x42 = 42.4115008234622

x43 = 80.1106126665397

x44 = 83.2522053201295

x45 = 10.9955742875643

x46 = -89.5353906273091

x47 = -58.1194640914112

x48 = -39.2699081698724

x49 = -86.3937979737193

x50 = 23.5619449019235

x51 = -17.2787595947439

x52 = 36.1283155162826

x53 = 92.6769832808989

x54 = -95.8185759344887

x55 = -70.6858347057703

x56 = 4.71238898038469

x57 = 51.8362787842316

x58 = -98.9601685880785

x59 = -32.9867228626928

x60 = 20.4203522483337

x61 = -4.71238898038469

x62 = -36.1283155162826

x63 = -158.650429006285

x64 = -51.8362787842316

x65 = -1.5707963267949

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