sin(4x)=0 (уравнение)

Найду корень уравнения: sin(4x)=0

Вы ввели

sin(4*x) = 0

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

Подробное решение

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

с изменением знака при 0

Получим:
$$\sin{\left(4 x \right)} = 0$$
Это ур-ние преобразуется в
$$4 x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$4 x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Или
$$4 x = 2 \pi n$$
$$4 x = 2 \pi n + \pi$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$4$$
получим ответ:
$$x_{1} = \frac{\pi n}{2}$$
$$x_{2} = \frac{\pi n}{2} + \frac{\pi}{4}$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     pi
x2 = --
     4 

$$x_{2} = \frac{\pi}{4}$$

Сумма и произведение корней

сумма

        pi
0 + 0 + --
        4 

$$\left(0 + 0\right) + \frac{\pi}{4}$$

=

pi
--
4 

$$\frac{\pi}{4}$$

произведение

    pi
1*0*--
    4 

$$1 \cdot 0 \frac{\pi}{4}$$

=

0

$$0$$

Численный ответ

x1 = 69.9004365423729

x2 = -45.553093477052

x3 = 10.9955742875643

x4 = 86.3937979737193

x5 = 50.2654824574367

x6 = 17.2787595947439

x7 = -69.1150383789755

x8 = 36.1283155162826

x9 = -99.7455667514759

x10 = -7.85398163397448

x11 = 95.8185759344887

x12 = -84.037603483527

x13 = -73.8274273593601

x14 = -23.5619449019235

x15 = -65.9734457253857

x16 = 87.9645943005142

x17 = -109.170344712245

x18 = -37.6991118430775

x19 = -21.9911485751286

x20 = -41.6261026600648

x21 = 76.1836218495525

x22 = -3.92699081698724

x23 = -36.1283155162826

x24 = -47.9092879672443

x25 = 68.329640215578

x26 = -58.1194640914112

x27 = 42.4115008234622

x28 = -40.0553063332699

x29 = -33.7721210260903

x30 = 25.9181393921158

x31 = 7.85398163397448

x32 = 28.2743338823081

x33 = -14.1371669411541

x34 = 62.0464549083984

x35 = -15.707963267949

x36 = 20.4203522483337

x37 = -51.8362787842316

x38 = -76.1836218495525

x39 = -77.7544181763474

x40 = 65.9734457253857

x41 = -85.6083998103219

x42 = 14.1371669411541

x43 = 32.2013246992954

x44 = 84.037603483527

x45 = 91.8915851175014

x46 = -69.9004365423729

x47 = 40.0553063332699

x48 = 72.2566310325652

x49 = -80.1106126665397

x50 = 90.3207887907066

x51 = -18.0641577581413

x52 = -1.5707963267949

x53 = 0.0

x54 = -55.7632696012188

x55 = 43.9822971502571

x56 = 80.1106126665397

x57 = -91.8915851175014

x58 = 21.9911485751286

x59 = -32.2013246992954

x60 = 64.4026493985908

x61 = -88.7499924639117

x62 = -10.9955742875643

x63 = -54.1924732744239

x64 = -43.9822971502571

x65 = 10.2101761241668

x66 = 58.1194640914112

x67 = -25.9181393921158

x68 = 3.92699081698724

x69 = -64.4026493985908

x70 = 54.1924732744239

x71 = -63.6172512351933

x72 = 181.426975744811

x73 = 18.0641577581413

x74 = 83.2522053201295

x75 = 6.28318530717959

x76 = -11.7809724509617

x77 = 2.35619449019234

x78 = 73.8274273593601

x79 = 54.9778714378214

x80 = -95.8185759344887

x81 = -19.6349540849362

x82 = 98.174770424681

x83 = 47.9092879672443

x84 = -59.6902604182061

x85 = 29.845130209103

x86 = -87.9645943005142

x87 = -62.0464549083984

x88 = 24.3473430653209

x89 = -98.174770424681

x90 = -29.845130209103

x91 = 46.3384916404494

x92 = 94.2477796076938

x93 = -81.6814089933346

x94 = 51.8362787842316

График