sin(x)=sin(3) (уравнение)

Найду корень уравнения: sin(x)=sin(3)

Вы ввели

sin(x) = sin(3)

$$\sin{\left(x \right)} = \sin{\left(3 \right)}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \sin{\left(3 \right)}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\sin{\left(3 \right)} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\sin{\left(3 \right)} \right)} + \pi$$
Или
$$x = 2 \pi n - 3 + \pi$$
$$x = 2 \pi n + 3$$
, где n - любое целое число

Быстрый ответ

x1 = 3

$$x_{1} = 3$$

x2 = -3 + pi

$$x_{2} = -3 + \pi$$

Сумма и произведение корней

сумма

0 + 3 + -3 + pi

$$\left(-3 + \pi\right) + \left(0 + 3\right)$$

=

pi

$$\pi$$

произведение

1*3*(-3 + pi)

$$1 \cdot 3 \left(-3 + \pi\right)$$

=

-9 + 3*pi

$$-9 + 3 \pi$$

Численный ответ

x1 = -103.814150222053

x2 = -53.5486677646163

x3 = 9.28318530717959

x4 = -131.805298797182

x5 = -100.389372261284

x6 = 21.8495559215388

x7 = 37.8407044966673

x8 = -3.28318530717959

x9 = 59.5486677646163

x10 = -62.6902604182061

x11 = 65.8318530717959

x12 = -56.4070751110265

x13 = -50.1238898038469

x14 = 81.8230016469244

x15 = -18.707963267949

x16 = 25.2743338823081

x17 = -40.9822971502571

x18 = -84.9645943005142

x19 = -37.5575191894877

x20 = 75.5398163397448

x21 = 0.141592653589793

x22 = 50.4070751110265

x23 = 94.3893722612836

x24 = -75.2566310325652

x25 = 90.9645943005142

x26 = -154.07963267949

x27 = -97.5309649148734

x28 = -94.106186954104

x29 = -24.9911485751286

x30 = -12.4247779607694

x31 = 78.398223686155

x32 = -68.9734457253857

x33 = 72.1150383789755

x34 = 62.9734457253857

x35 = -15.8495559215388

x36 = 84.6814089933346

x37 = 40.6991118430775

x38 = 46.9822971502571

x39 = 53.2654824574367

x40 = 88.106186954104

x41 = 28.1327412287183

x42 = 6.42477796076938

x43 = 18.9911485751286

x44 = 100.672557568463

x45 = -31.2743338823081

x46 = -119.238928182822

x47 = -47.2654824574367

x48 = -78.6814089933346

x49 = 31.5575191894877

x50 = 34.4159265358979

x51 = 15.5663706143592

x52 = -22.1327412287183

x53 = -66.1150383789755

x54 = -43.8407044966673

x55 = -28.4159265358979

x56 = -34.6991118430775

x57 = -59.8318530717959

x58 = -81.5398163397448

x59 = -6.14159265358979

x60 = 3.0

x61 = -9.56637061435917

x62 = 44.1238898038469

x63 = 69.2566310325652

x64 = -72.398223686155

x65 = -87.8230016469244

x66 = 33115.3865688364

x67 = 56.6902604182061

x68 = -91.2477796076938

x69 = 97.2477796076938

x70 = 12.707963267949

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