sin(8*x)=0 (уравнение)

Найду корень уравнения: sin(8*x)=0

Вы ввели

sin(8*x) = 0

$$\sin{\left(8 x \right)} = 0$$

Подробное решение

Дано уравнение
$$\sin{\left(8 x \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$\sin{\left(8 x \right)} = 0$$
Это ур-ние преобразуется в
$$8 x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$8 x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Или
$$8 x = 2 \pi n$$
$$8 x = 2 \pi n + \pi$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$8$$
получим ответ:
$$x_{1} = \frac{\pi n}{4}$$
$$x_{2} = \frac{\pi n}{4} + \frac{\pi}{8}$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     pi
x2 = --
     8 

$$x_{2} = \frac{\pi}{8}$$

Сумма и произведение корней

сумма

        pi
0 + 0 + --
        8 

$$\left(0 + 0\right) + \frac{\pi}{8}$$

=

pi
--
8 

$$\frac{\pi}{8}$$

произведение

    pi
1*0*--
    8 

$$1 \cdot 0 \frac{\pi}{8}$$

=

0

$$0$$

Численный ответ

x1 = 64.009950316892

x2 = 92.2842841992002

x3 = -71.8639319508665

x4 = -5.89048622548086

x5 = 12.1736715326604

x6 = -79.717913584841

x7 = 96.2112750161874

x8 = 56.1559686829176

x9 = 67.1515429704818

x10 = -31.8086256175967

x11 = 48.6946861306418

x12 = -93.8550805259951

x13 = 80.1106126665397

x14 = -34.5575191894877

x15 = 87.9645943005142

x16 = 10.2101761241668

x17 = 30.2378292908018

x18 = -37.6991118430775

x19 = 27.4889357189107

x20 = 32.2013246992954

x21 = 36.1283155162826

x22 = -13.7444678594553

x23 = 65.9734457253857

x24 = -62.0464549083984

x25 = 60.0829594999048

x26 = -1.96349540849362

x27 = -51.8362787842316

x28 = -60.8683576633022

x29 = 52.2289778659303

x30 = -69.9004365423729

x31 = -55.7632696012188

x32 = 84.037603483527

x33 = 54.1924732744239

x34 = 111.919238284136

x35 = 20.0276531666349

x36 = 82.0741080750334

x37 = -73.8274273593601

x38 = -31.4159265358979

x39 = 58.1194640914112

x40 = 100.138265833175

x41 = 98.174770424681

x42 = -47.9092879672443

x43 = -91.8915851175014

x44 = 38.0918109247762

x45 = 70.2931356240716

x46 = 74.2201264410589

x47 = 21.9911485751286

x48 = -89.9280897090078

x49 = -33.7721210260903

x50 = 50.2654824574367

x51 = 8.24668071567321

x52 = 76.1836218495525

x53 = -99.7455667514759

x54 = 78.1471172580461

x55 = -77.7544181763474

x56 = -15.707963267949

x57 = -3.92699081698724

x58 = 1.96349540849362

x59 = -20.0276531666349

x60 = -7.85398163397448

x61 = -35.7356164345839

x62 = -75.7909227678538

x63 = -64.009950316892

x64 = -29.845130209103

x65 = 45.553093477052

x66 = 28.2743338823081

x67 = 43.9822971502571

x68 = -45.9457925587507

x69 = -21.9911485751286

x70 = 94.2477796076938

x71 = -87.9645943005142

x72 = -42.0188017417635

x73 = -97.7820713429823

x74 = -11.7809724509617

x75 = 62.0464549083984

x76 = 42.0188017417635

x77 = 9.8174770424681

x78 = -25.9181393921158

x79 = 18.0641577581413

x80 = 16.1006623496477

x81 = -65.9734457253857

x82 = -57.7267650097125

x83 = 6.28318530717959

x84 = 14.1371669411541

x85 = -9.8174770424681

x86 = 34.164820107789

x87 = 0.0

x88 = -27.8816348006094

x89 = 72.2566310325652

x90 = -67.9369411338793

x91 = 23.9546439836222

x92 = -23.9546439836222

x93 = -95.8185759344887

x94 = -43.9822971502571

x95 = -84.037603483527

x96 = -49.872783375738

x97 = -86.0010988920206

x98 = 40.0553063332699

x99 = 86.0010988920206

x100 = -53.7997741927252

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