sin(x)=sin(-x) (уравнение)

Найду корень уравнения: sin(x)=sin(-x)

Вы ввели

sin(x) = sin(-x)

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

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \sin{\left(- x \right)}$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 2

Ур-ние превратится в
$$\sin{\left(x \right)} = 0$$
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Или
$$x = 2 \pi n$$
$$x = 2 \pi n + \pi$$
, где n - любое целое число

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 = -6.28318530717959

x2 = -78.5398163397448

x3 = -81.6814089933346

x4 = -97.3893722612836

x5 = -69.1150383789755

x6 = 12.5663706143592

x7 = -62.8318530717959

x8 = 56.5486677646163

x9 = -21.9911485751286

x10 = -34.5575191894877

x11 = -113.097335529233

x12 = -56.5486677646163

x13 = -31.4159265358979

x14 = 91.106186954104

x15 = 47.1238898038469

x16 = -53.4070751110265

x17 = -72.2566310325652

x18 = 0.0

x19 = -43.9822971502571

x20 = 50.2654824574367

x21 = 69.1150383789755

x22 = 6.28318530717959

x23 = 43.9822971502571

x24 = -9.42477796076938

x25 = 40.8407044966673

x26 = 15.707963267949

x27 = 18.8495559215388

x28 = 37.6991118430775

x29 = -59.6902604182061

x30 = 87.9645943005142

x31 = -91.106186954104

x32 = 25.1327412287183

x33 = -18.8495559215388

x34 = 28.2743338823081

x35 = -65.9734457253857

x36 = 62.8318530717959

x37 = -87.9645943005142

x38 = -25.1327412287183

x39 = 21.9911485751286

x40 = -75.398223686155

x41 = -15.707963267949

x42 = -50.2654824574367

x43 = 53.4070751110265

x44 = -100.530964914873

x45 = -232.477856365645

x46 = 75.398223686155

x47 = 72.2566310325652

x48 = -2642.07942166902

x49 = -37.6991118430775

x50 = 34.5575191894877

x51 = 81.6814089933346

x52 = -94.2477796076938

x53 = 65.9734457253857

x54 = 3.14159265358979

x55 = -12.5663706143592

x56 = 78.5398163397448

x57 = 9.42477796076938

x58 = 97.3893722612836

x59 = -84.8230016469244

x60 = -28.2743338823081

x61 = 84.8230016469244

x62 = 100.530964914873

x63 = -267.035375555132

x64 = 94.2477796076938

x65 = -3.14159265358979

x66 = -40.8407044966673

x67 = 59.6902604182061

x68 = -47.1238898038469

x69 = 31.4159265358979

График