log(sin(x)+1)=0 (уравнение)

Найду корень уравнения: log(sin(x)+1)=0

Вы ввели

log(sin(x) + 1) = 0

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

Подробное решение

Дано уравнение
$$\log{\left(\sin{\left(x \right)} + 1 \right)} = 0$$
преобразуем
$$\log{\left(\sin{\left(x \right)} + 1 \right)} = 0$$
$$\log{\left(\sin{\left(x \right)} + 1 \right)} + 0 = 0$$
Сделаем замену
$$w = \sin{\left(x \right)}$$
Дано уравнение
$$\log{\left(w + 1 \right)} = 0$$
$$\log{\left(w + 1 \right)} = 0$$
Это уравнение вида:

log(v)=p

По определению log

v=e^p

тогда
$$1 w + 1 = e^{\frac{0}{1}}$$
упрощаем
$$w + 1 = 1$$
$$w = 0$$
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:

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

x2 = pi

$$x_{2} = \pi$$

Сумма и произведение корней

сумма

0 + 0 + pi

$$\left(0 + 0\right) + \pi$$

=

pi

$$\pi$$

произведение

1*0*pi

$$1 \cdot 0 \pi$$

=

0

$$0$$

Численный ответ

x1 = -100.530964914873

x2 = -78.5398163397448

x3 = 97.3893722612836

x4 = 128.805298797182

x5 = 18.8495559215388

x6 = -94.2477796076938

x7 = -65.9734457253857

x8 = -56.5486677646163

x9 = 56.5486677646163

x10 = 6.28318530717959

x11 = -69.1150383789755

x12 = 78.5398163397448

x13 = -3.14159265358979

x14 = -21.9911485751286

x15 = 81.6814089933346

x16 = -91.106186954104

x17 = 87417.9571787896

x18 = -62.8318530717959

x19 = -31.4159265358979

x20 = 0.0

x21 = 62.8318530717959

x22 = 84.8230016469244

x23 = 596.902604182061

x24 = 72.2566310325652

x25 = 91.106186954104

x26 = -18.8495559215388

x27 = -9.42477796076938

x28 = 28.2743338823081

x29 = 43.9822971502571

x30 = -6.28318530717959

x31 = -34.5575191894877

x32 = -59.6902604182061

x33 = -53.4070751110265

x34 = 87.9645943005142

x35 = 69.1150383789755

x36 = -292.168116783851

x37 = -75.398223686155

x38 = 75.398223686155

x39 = -84.8230016469244

x40 = 3.14159265358979

x41 = -37.6991118430775

x42 = 94.2477796076938

x43 = 21.9911485751286

x44 = -87.9645943005142

x45 = 100.530964914873

x46 = -25.1327412287183

x47 = 50.2654824574367

x48 = -43.9822971502571

x49 = 65.9734457253857

x50 = 9.42477796076938

x51 = 40.8407044966673

x52 = 37.6991118430775

x53 = -28.2743338823081

x54 = 53.4070751110265

x55 = -40.8407044966673

x56 = 47.1238898038469

x57 = -50.2654824574367

x58 = -97.3893722612836

x59 = 15.707963267949

x60 = 25.1327412287183

x61 = -12.5663706143592

x62 = 31.4159265358979

x63 = 12.5663706143592

x64 = 59.6902604182061

x65 = -15.707963267949

x66 = -81.6814089933346

x67 = -72.2566310325652

x68 = 34.5575191894877

x69 = -47.1238898038469

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