atan(sin(x)) = 0 (уравнение)

Найду корень уравнения: atan(sin(x)) = 0

Вы ввели

atan(sin(x)) = 0

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

Подробное решение

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

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

x2 = pi

$$x_{2} = \pi$$

Численный ответ

x1 = -75.398223686155

x2 = 389.557489045134

x3 = 34.5575191894877

x4 = -59784.5081978138

x5 = -84.8230016469244

x6 = 28.2743338823081

x7 = 9.42477796076938

x8 = -15.707963267949

x9 = 37.6991118430775

x10 = 43.9822971502571

x11 = -6.28318530717959

x12 = 18.8495559215388

x13 = 81.6814089933346

x14 = -94.2477796076938

x15 = 25.1327412287183

x16 = -31.4159265358979

x17 = -69.1150383789755

x18 = -72.2566310325652

x19 = -53.4070751110265

x20 = 84.8230016469244

x21 = 6.28318530717959

x22 = -50.2654824574367

x23 = -56.5486677646163

x24 = -131.946891450771

x25 = 50.2654824574367

x26 = 21.9911485751286

x27 = -12.5663706143592

x28 = -3.14159265358979

x29 = -25.1327412287183

x30 = 62.8318530717959

x31 = 56.5486677646163

x32 = 12.5663706143592

x33 = 75.398223686155

x34 = 3.14159265358979

x35 = -97.3893722612836

x36 = 0.0

x37 = -37.6991118430775

x38 = -100.530964914873

x39 = -34.5575191894877

x40 = 5274.73406537726

x41 = -43.9822971502571

x42 = -65.9734457253857

x43 = 31.4159265358979

x44 = -119.380520836412

x45 = -78.5398163397448

x46 = -9.42477796076938

x47 = 69.1150383789755

x48 = 94.2477796076938

x49 = 47.1238898038469

x50 = -21.9911485751286

x51 = 706.858347057703

x52 = 103.672557568463

x53 = -62.8318530717959

x54 = 59.6902604182061

x55 = 97.3893722612836

x56 = 40.8407044966673

x57 = -81.6814089933346

x58 = -40.8407044966673

x59 = 78.5398163397448

x60 = -59.6902604182061

x61 = 182.212373908208

x62 = -87.9645943005142

x63 = -91.106186954104

x64 = -47.1238898038469

x65 = 72.2566310325652

x66 = -28.2743338823081

x67 = 53.4070751110265

x68 = -18.8495559215388

x69 = 15.707963267949

x70 = 87.9645943005142

x71 = 65.9734457253857

x72 = 91.106186954104

x73 = 100.530964914873

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