3sin(2x)= 0 (уравнение)

Найду корень уравнения: 3sin(2x)= 0

Вы ввели

3*sin(2*x) = 0

$$3 \sin{\left(2 x \right)} = 0$$

Подробное решение

Дано уравнение
$$3 \sin{\left(2 x \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$3 \sin{\left(2 x \right)} = 0$$

Разделим обе части ур-ния на 3

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 

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

Численный ответ

x1 = -75.398223686155

x2 = -95.8185759344887

x3 = 73.8274273593601

x4 = 34.5575191894877

x5 = -94.2477796076938

x6 = -31.4159265358979

x7 = 26.7035375555132

x8 = 92.6769832808989

x9 = 14.1371669411541

x10 = 64.4026493985908

x11 = -50.2654824574367

x12 = -86.3937979737193

x13 = 50.2654824574367

x14 = -67.5442420521806

x15 = -43.9822971502571

x16 = 31.4159265358979

x17 = 1.5707963267949

x18 = 94.2477796076938

x19 = -36.1283155162826

x20 = 70.6858347057703

x21 = -20.4203522483337

x22 = -28.2743338823081

x23 = -61.261056745001

x24 = 113.097335529233

x25 = 65.9734457253857

x26 = 86.3937979737193

x27 = -21.9911485751286

x28 = -9787.631912259

x29 = -15.707963267949

x30 = -6.28318530717959

x31 = -80.1106126665397

x32 = -72.2566310325652

x33 = -53.4070751110265

x34 = -39.2699081698724

x35 = 36.1283155162826

x36 = 21.9911485751286

x37 = -42.4115008234622

x38 = -97.3893722612836

x39 = -37.6991118430775

x40 = 48.6946861306418

x41 = -17.2787595947439

x42 = -9.42477796076938

x43 = -81.6814089933346

x44 = -23.5619449019235

x45 = -87.9645943005142

x46 = 72.2566310325652

x47 = 15.707963267949

x48 = 29.845130209103

x49 = 58.1194640914112

x50 = 51.8362787842316

x51 = -51.8362787842316

x52 = -29.845130209103

x53 = 6.28318530717959

x54 = 95.8185759344887

x55 = -45.553093477052

x56 = -89.5353906273091

x57 = 56.5486677646163

x58 = -119.380520836412

x59 = -48.6946861306418

x60 = 80.1106126665397

x61 = -83.2522053201295

x62 = 59.6902604182061

x63 = 45.553093477052

x64 = -40.8407044966673

x65 = 78.5398163397448

x66 = -59.6902604182061

x67 = 67.5442420521806

x68 = -73.8274273593601

x69 = 100.530964914873

x70 = 42.4115008234622

x71 = -1.5707963267949

x72 = 28.2743338823081

x73 = 81.6814089933346

x74 = 43.9822971502571

x75 = -58.1194640914112

x76 = 37.6991118430775

x77 = 590.619418874881

x78 = 23.5619449019235

x79 = -7.85398163397448

x80 = 89.5353906273091

x81 = -64.4026493985908

x82 = 20.4203522483337

x83 = -14.1371669411541

x84 = 12.5663706143592

x85 = 0.0

x86 = -65.9734457253857

x87 = 4.71238898038469

x88 = 87.9645943005142

x89 = 7.85398163397448

График