sin(2*x)=0 (уравнение)

Найду корень уравнения: sin(2*x)=0

Вы ввели

sin(2*x) = 0

$$\sin{\left(2 x \right)} = 0$$

Подробное решение

Дано уравнение
$$\sin{\left(2 x \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$\sin{\left(2 x \right)} = 0$$
Это ур-ние преобразуется в
$$2 x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Или
$$2 x = 2 \pi n$$
$$2 x = 2 \pi n + \pi$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = \pi n$$
$$x_{2} = \pi n + \frac{\pi}{2}$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     pi
x2 = --
     2 

$$x_{2} = \frac{\pi}{2}$$

Сумма и произведение корней

сумма

        pi
0 + 0 + --
        2 

$$\left(0 + 0\right) + \frac{\pi}{2}$$

=

pi
--
2 

$$\frac{\pi}{2}$$

произведение

    pi
1*0*--
    2 

$$1 \cdot 0 \frac{\pi}{2}$$

=

0

$$0$$

Численный ответ

x1 = 64.4026493985908

x2 = 73.8274273593601

x3 = 89.5353906273091

x4 = 56.5486677646163

x5 = 81.6814089933346

x6 = 48.6946861306418

x7 = 80.1106126665397

x8 = -6.28318530717959

x9 = -89.5353906273091

x10 = -59.6902604182061

x11 = 87.9645943005142

x12 = -58.1194640914112

x13 = 100.530964914873

x14 = -37.6991118430775

x15 = 23.5619449019235

x16 = 92.6769832808989

x17 = 590.619418874881

x18 = 36.1283155162826

x19 = 4.71238898038469

x20 = 65.9734457253857

x21 = -40.8407044966673

x22 = -50.2654824574367

x23 = 15.707963267949

x24 = 12.5663706143592

x25 = 26.7035375555132

x26 = 59.6902604182061

x27 = -51.8362787842316

x28 = -1.5707963267949

x29 = -23.5619449019235

x30 = -45.553093477052

x31 = -64.4026493985908

x32 = -73.8274273593601

x33 = -14.1371669411541

x34 = -31.4159265358979

x35 = 58.1194640914112

x36 = -48.6946861306418

x37 = -9.42477796076938

x38 = -53.4070751110265

x39 = -75.398223686155

x40 = 21.9911485751286

x41 = -17.2787595947439

x42 = 50.2654824574367

x43 = 51.8362787842316

x44 = -97.3893722612836

x45 = -15.707963267949

x46 = 70.6858347057703

x47 = -83.2522053201295

x48 = -7.85398163397448

x49 = 7.85398163397448

x50 = -67.5442420521806

x51 = -61.261056745001

x52 = -29.845130209103

x53 = 45.553093477052

x54 = 28.2743338823081

x55 = 43.9822971502571

x56 = -119.380520836412

x57 = 113.097335529233

x58 = -21.9911485751286

x59 = 94.2477796076938

x60 = -87.9645943005142

x61 = 37.6991118430775

x62 = -28.2743338823081

x63 = -42.4115008234622

x64 = 95.8185759344887

x65 = 67.5442420521806

x66 = 1.5707963267949

x67 = -65.9734457253857

x68 = -94.2477796076938

x69 = -20.4203522483337

x70 = 6.28318530717959

x71 = 86.3937979737193

x72 = 78.5398163397448

x73 = 14.1371669411541

x74 = -80.1106126665397

x75 = 0.0

x76 = 29.845130209103

x77 = 72.2566310325652

x78 = 42.4115008234622

x79 = -86.3937979737193

x80 = -39.2699081698724

x81 = -95.8185759344887

x82 = -43.9822971502571

x83 = -483.805268652828

x84 = 20.4203522483337

x85 = -36.1283155162826

x86 = 31.4159265358979

x87 = -81.6814089933346

x88 = -72.2566310325652

x89 = 34.5575191894877

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