sin(sin(x))=0 (уравнение)

Найду корень уравнения: sin(sin(x))=0

Вы ввели

sin(sin(x)) = 0

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

Подробное решение

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

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

x2 = pi

$$x_{2} = \pi$$

x3 = pi - re(asin(pi)) - I*im(asin(pi))

$$x_{3} = - \operatorname{re}{\left(\operatorname{asin}{\left(\pi \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\pi \right)}\right)}$$

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

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

Сумма и произведение корней

сумма

0 + 0 + pi + pi - re(asin(pi)) - I*im(asin(pi)) + I*im(asin(pi)) + re(asin(pi))

$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(\pi \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\pi \right)}\right)}\right) - \left(- 2 \pi + \operatorname{re}{\left(\operatorname{asin}{\left(\pi \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\pi \right)}\right)}\right)$$

=

2*pi

$$2 \pi$$

произведение

1*0*pi*(pi - re(asin(pi)) - I*im(asin(pi)))*(I*im(asin(pi)) + re(asin(pi)))

$$1 \cdot 0 \pi \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\pi \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\pi \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\pi \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\pi \right)}\right)}\right)$$

=

0

$$0$$

Численный ответ

x1 = -84.8230016469244

x2 = -12.5663706143592

x3 = 75.398223686155

x4 = -50.2654824574367

x5 = -97.3893722612836

x6 = 3.14159265358979

x7 = 15.707963267949

x8 = 59.6902604182061

x9 = 40.8407044966673

x10 = -62.8318530717959

x11 = 21.9911485751286

x12 = -53.4070751110265

x13 = -72.2566310325652

x14 = 9.42477796076938

x15 = 87.9645943005142

x16 = -91.106186954104

x17 = -100.530964914873

x18 = -34.5575191894877

x19 = -47.1238898038469

x20 = -87.9645943005142

x21 = 0.0

x22 = 13540.264336972

x23 = 29666.0594278484

x24 = -21.9911485751286

x25 = 37.6991118430775

x26 = -116.238928182822

x27 = -28.2743338823081

x28 = -6.28318530717959

x29 = 43.9822971502571

x30 = 91.106186954104

x31 = -56.5486677646163

x32 = -40.8407044966673

x33 = 94.2477796076938

x34 = -31.4159265358979

x35 = -69.1150383789755

x36 = 47.1238898038469

x37 = 62.8318530717959

x38 = 18.8495559215388

x39 = -37.6991118430775

x40 = -2667.21216289773

x41 = 56.5486677646163

x42 = 65.9734457253857

x43 = -59.6902604182061

x44 = -75.398223686155

x45 = -3.14159265358979

x46 = 81.6814089933346

x47 = -18.8495559215388

x48 = 31.4159265358979

x49 = 109.955742875643

x50 = 2921.68116783851

x51 = -9.42477796076938

x52 = -15.707963267949

x53 = -43.9822971502571

x54 = 78.5398163397448

x55 = -78.5398163397448

x56 = -81.6814089933346

x57 = 84.8230016469244

x58 = 28.2743338823081

x59 = -25.1327412287183

x60 = -65.9734457253857

x61 = 97.3893722612836

x62 = 69.1150383789755

x63 = 50.2654824574367

x64 = 100.530964914873

x65 = 34.5575191894877

x66 = 6.28318530717959

x67 = 25.1327412287183

x68 = -131.946891450771

x69 = 53.4070751110265

x70 = -94.2477796076938

x71 = 12.5663706143592

x72 = 72.2566310325652

График