sinx×(x+1) (уравнение)

Найду корень уравнения: sinx×(x+1)

Вы ввели

sin(x)*(x + 1) = 0

$$\left(x + 1\right) \sin{\left(x \right)} = 0$$

Подробное решение

Дано уравнение
$$\left(x + 1\right) \sin{\left(x \right)} = 0$$
преобразуем
$$\left(x + 1\right) \sin{\left(x \right)} = 0$$
$$\left(x + 1\right) \sin{\left(x \right)} = 0$$
Сделаем замену
$$w = \sin{\left(x \right)}$$
Раскрываем скобочки в левой части ур-ния

wx+1 = 0

Разделим обе части ур-ния на 1 + x

w = 0 / (1 + x)

Получим ответ: w = 0
делаем обратную замену
$$\sin{\left(x \right)} = w$$
Дано уравнение
$$\sin{\left(x \right)} = w$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, где n - любое целое число
подставляем w:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$x_{1} = 2 \pi n$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
$$x_{2} = 2 \pi n + \pi$$

Быстрый ответ

x1 = -1

$$x_{1} = -1$$

x2 = 0

$$x_{2} = 0$$

x3 = pi

$$x_{3} = \pi$$

Численный ответ

x1 = -72.2566310325652

x2 = -78.5398163397448

x3 = -25.1327412287183

x4 = -97.3893722612836

x5 = -65.9734457253857

x6 = 56.5486677646163

x7 = 43.9822971502571

x8 = 0.0

x9 = 62.8318530717959

x10 = 31.4159265358979

x11 = 100.530964914873

x12 = -87.9645943005142

x13 = -81.6814089933346

x14 = 18.8495559215388

x15 = 78.5398163397448

x16 = -6.28318530717959

x17 = -12.5663706143592

x18 = -56.5486677646163

x19 = 87.9645943005142

x20 = -47.1238898038469

x21 = 50.2654824574367

x22 = -1.0

x23 = -53.4070751110265

x24 = 75.398223686155

x25 = -43.9822971502571

x26 = 81.6814089933346

x27 = -59.6902604182061

x28 = 65.9734457253857

x29 = -103.672557568463

x30 = 12.5663706143592

x31 = 21.9911485751286

x32 = -31.4159265358979

x33 = -40.8407044966673

x34 = 72.2566310325652

x35 = 47.1238898038469

x36 = 9.42477796076938

x37 = -100.530964914873

x38 = 28.2743338823081

x39 = 94.2477796076938

x40 = -21.9911485751286

x41 = 53.4070751110265

x42 = -94.2477796076938

x43 = -18.8495559215388

x44 = 40.8407044966673

x45 = -15.707963267949

x46 = 3.14159265358979

x47 = 84.8230016469244

x48 = -37.6991118430775

x49 = 6.28318530717959

x50 = 37.6991118430775

x51 = -34.5575191894877

x52 = -62.8318530717959

x53 = -91.106186954104

x54 = -28.2743338823081

x55 = -9.42477796076938

x56 = 59.6902604182061

x57 = -50.2654824574367

x58 = 25.1327412287183

x59 = 91.106186954104

x60 = 69.1150383789755

x61 = 15.707963267949

x62 = 97.3893722612836

x63 = -69.1150383789755

x64 = -84.8230016469244

x65 = -75.398223686155

x66 = 34.5575191894877

x67 = -3.14159265358979

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