3tg2x=0 (уравнение)

Найду корень уравнения: 3tg2x=0

Вы ввели

3*tan(2*x) = 0

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

Подробное решение

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

с изменением знака при 0

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

Разделим обе части ур-ния на 3

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

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

Сумма и произведение корней

сумма

0 + 0

$$0 + 0$$

=

0

$$0$$

произведение

1*0

$$1 \cdot 0$$

=

0

$$0$$

Численный ответ

x1 = -12.5663706143592

x2 = 75.398223686155

x3 = 36.1283155162826

x4 = 59.6902604182061

x5 = 40.8407044966673

x6 = 67.5442420521806

x7 = 21.9911485751286

x8 = 89.5353906273091

x9 = 23.5619449019235

x10 = 70.6858347057703

x11 = -87.9645943005142

x12 = -14.1371669411541

x13 = -69.1150383789755

x14 = 4.71238898038469

x15 = 26.7035375555132

x16 = 56.5486677646163

x17 = 92.6769832808989

x18 = -75.398223686155

x19 = -43.9822971502571

x20 = -83.2522053201295

x21 = 42.4115008234622

x22 = -95.8185759344887

x23 = -1.5707963267949

x24 = -39.2699081698724

x25 = 97.3893722612836

x26 = 58.1194640914112

x27 = 6.28318530717959

x28 = 45.553093477052

x29 = 14.1371669411541

x30 = 72.2566310325652

x31 = -58.1194640914112

x32 = -86.3937979737193

x33 = -53.4070751110265

x34 = -72.2566310325652

x35 = -100.530964914873

x36 = -34.5575191894877

x37 = -47.1238898038469

x38 = 86.3937979737193

x39 = 48.6946861306418

x40 = -21.9911485751286

x41 = -7.85398163397448

x42 = -31.4159265358979

x43 = -42.4115008234622

x44 = 18.8495559215388

x45 = -17.2787595947439

x46 = -3.14159265358979

x47 = -78.5398163397448

x48 = -25.1327412287183

x49 = 34.5575191894877

x50 = 95.8185759344887

x51 = -80.1106126665397

x52 = -45.553093477052

x53 = -94.2477796076938

x54 = 12.5663706143592

x55 = -50.2654824574367

x56 = -97.3893722612836

x57 = -89.5353906273091

x58 = 15.707963267949

x59 = 51.8362787842316

x60 = 9.42477796076938

x61 = 0.0

x62 = -61.261056745001

x63 = 73.8274273593601

x64 = 29.845130209103

x65 = 1.5707963267949

x66 = 62.8318530717959

x67 = -37.6991118430775

x68 = 65.9734457253857

x69 = 81.6814089933346

x70 = 31.4159265358979

x71 = -20.4203522483337

x72 = -81.6814089933346

x73 = 28.2743338823081

x74 = -29.845130209103

x75 = -23.5619449019235

x76 = 100.530964914873

x77 = -67.5442420521806

x78 = -64.4026493985908

x79 = 87.9645943005142

x80 = -91.106186954104

x81 = 64.4026493985908

x82 = 37.6991118430775

x83 = -28.2743338823081

x84 = -6.28318530717959

x85 = 43.9822971502571

x86 = -56.5486677646163

x87 = -73.8274273593601

x88 = 94.2477796076938

x89 = -59.6902604182061

x90 = -51.8362787842316

x91 = -9.42477796076938

x92 = -15.707963267949

x93 = 80.1106126665397

x94 = 78.5398163397448

x95 = 7.85398163397448

x96 = 84.8230016469244

x97 = -65.9734457253857

x98 = 50.2654824574367

x99 = 20.4203522483337

x100 = -36.1283155162826

x101 = 53.4070751110265

График