2sin(2x-4π)=0 (уравнение)

Найду корень уравнения: 2sin(2x-4π)=0

Вы ввели

2*sin(2*x - 4*pi) = 0

$$2 \sin{\left(2 x - 4 \pi \right)} = 0$$

Подробное решение

Дано уравнение
$$2 \sin{\left(2 x - 4 \pi \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$2 \sin{\left(2 x - 4 \pi \right)} = 0$$

Разделим обе части ур-ния на 2

Ур-ние превратится в
$$\sin{\left(2 x \right)} = 0$$
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
--
2 

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

=

pi
--
2 

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

произведение

  pi
0*--
  2 

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

=

0

$$0$$

Численный ответ

x1 = -53.4070751110265

x2 = -43.9822971502571

x3 = 72.2566310325652

x4 = -20.4203522483337

x5 = -29.845130209103

x6 = 51.8362787842316

x7 = -119.380520836412

x8 = -95.8185759344887

x9 = -83.2522053201295

x10 = -15.707963267949

x11 = -67.5442420521806

x12 = -42.4115008234622

x13 = 21.9911485751286

x14 = 29.845130209103

x15 = 23.5619449019235

x16 = 15.707963267949

x17 = 50.2654824574367

x18 = 89.5353906273091

x19 = 26.7035375555132

x20 = -50.2654824574367

x21 = -65.9734457253857

x22 = 95.8185759344887

x23 = 31.4159265358979

x24 = -40.8407044966673

x25 = 0.0

x26 = 48.6946861306418

x27 = 4.71238898038469

x28 = 65.9734457253857

x29 = -31.4159265358979

x30 = 42.4115008234622

x31 = -39.2699081698724

x32 = -1.5707963267949

x33 = 81.6814089933346

x34 = -59.6902604182061

x35 = -6.28318530717959

x36 = -9.42477796076938

x37 = -73.8274273593601

x38 = -97.3893722612836

x39 = -17.2787595947439

x40 = -28.2743338823081

x41 = -64.4026493985908

x42 = -89.5353906273091

x43 = 86.3937979737193

x44 = -21.9911485751286

x45 = 590.619418874881

x46 = 20.4203522483337

x47 = 113.097335529233

x48 = 6.28318530717959

x49 = 64.4026493985908

x50 = -14.1371669411541

x51 = -94.2477796076938

x52 = -51.8362787842316

x53 = -81.6814089933346

x54 = -48.6946861306418

x55 = 87.9645943005142

x56 = -75.398223686155

x57 = 37.6991118430775

x58 = -86.3937979737193

x59 = 78.5398163397448

x60 = 34.5575191894877

x61 = -72.2566310325652

x62 = 43.9822971502571

x63 = -80.1106126665397

x64 = 7.85398163397448

x65 = 100.530964914873

x66 = -23.5619449019235

x67 = 92.6769832808989

x68 = -37.6991118430775

x69 = 14.1371669411541

x70 = 80.1106126665397

x71 = 56.5486677646163

x72 = -87.9645943005142

x73 = 73.8274273593601

x74 = -483.805268652828

x75 = 45.553093477052

x76 = -61.261056745001

x77 = 36.1283155162826

x78 = 12.5663706143592

x79 = -7.85398163397448

x80 = 67.5442420521806

x81 = 28.2743338823081

x82 = 1.5707963267949

x83 = -58.1194640914112

x84 = 58.1194640914112

x85 = -45.553093477052

x86 = 59.6902604182061

x87 = 70.6858347057703

x88 = -36.1283155162826

x89 = 94.2477796076938

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