sin(10*x)=0 (уравнение)

Найду корень уравнения: sin(10*x)=0

Вы ввели

sin(10*x) = 0

$$\sin{\left(10 x \right)} = 0$$

Подробное решение

Дано уравнение
$$\sin{\left(10 x \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$\sin{\left(10 x \right)} = 0$$
Это ур-ние преобразуется в
$$10 x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$10 x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Или
$$10 x = 2 \pi n$$
$$10 x = 2 \pi n + \pi$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$10$$
получим ответ:
$$x_{1} = \frac{\pi n}{5}$$
$$x_{2} = \frac{\pi n}{5} + \frac{\pi}{10}$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     pi
x2 = --
     10

$$x_{2} = \frac{\pi}{10}$$

Сумма и произведение корней

сумма

        pi
0 + 0 + --
        10

$$\left(0 + 0\right) + \frac{\pi}{10}$$

=

pi
--
10

$$\frac{\pi}{10}$$

произведение

    pi
1*0*--
    10

$$1 \cdot 0 \frac{\pi}{10}$$

=

0

$$0$$

Численный ответ

x1 = -61.8893752757189

x2 = 20.1061929829747

x3 = -41.7831822927443

x4 = 46.18141200777

x5 = 78.2256570743859

x6 = -77.9114978090269

x7 = -16.0221225333079

x8 = -99.9026463841554

x9 = -3.76991118430775

x10 = -83.8805238508475

x11 = 80.1106126665397

x12 = 34.2433599241287

x13 = 88.5929128312322

x14 = 60.0044196835651

x15 = -71.9424717672063

x16 = -27.9601746169492

x17 = 36.1283155162826

x18 = 76.026542216873

x19 = -13.8230076757951

x20 = 42.0973415581032

x21 = -57.8053048260522

x22 = -38.0132711084365

x23 = -51.8362787842316

x24 = 18.2212373908208

x25 = 40.2123859659494

x26 = -73.8274273593601

x27 = 70.0575161750524

x28 = 58.1194640914112

x29 = 30.159289474462

x30 = 92.0486647501809

x31 = -53.4070751110265

x32 = -91.734505484822

x33 = -1.88495559215388

x34 = -93.9336203423348

x35 = 21.9911485751286

x36 = 50.2654824574367

x37 = -136.659280431156

x38 = -23.8761041672824

x39 = -17.9070781254618

x40 = -19.7920337176157

x41 = -60.0044196835651

x42 = 12.2522113490002

x43 = 81.9955682586936

x44 = -45.867252742411

x45 = 86.0796387083603

x46 = -25.7610597594363

x47 = -85.7654794430014

x48 = 52.1504380495906

x49 = -7.85398163397448

x50 = -81.9955682586936

x51 = 56.2345084992573

x52 = 48.0663675999238

x53 = -29.845130209103

x54 = 38.0132711084365

x55 = 43.9822971502571

x56 = -21.9911485751286

x57 = 16.0221225333079

x58 = -63.7743308678728

x59 = 68.1725605828985

x60 = 94.2477796076938

x61 = 100.216805649514

x62 = -87.9645943005142

x63 = -55.9203492338983

x64 = 26.0752190247953

x65 = 96.1327351998477

x66 = 37.6991118430775

x67 = -9.73893722612836

x68 = -39.8982267005904

x69 = 74.1415866247191

x70 = -35.8141562509236

x71 = -5.96902604182061

x72 = 64.0884901332318

x73 = -65.9734457253857

x74 = 32.0442450666159

x75 = 90.1637091580271

x76 = 14.1371669411541

x77 = 84.1946831162065

x78 = 2.19911485751286

x79 = 0.0

x80 = -69.7433569096934

x81 = 8.16814089933346

x82 = -89.8495498926681

x83 = 72.2566310325652

x84 = 62.2035345410779

x85 = -11.9380520836412

x86 = 54.0353936417444

x87 = -33.9292006587698

x88 = -98.0176907920015

x89 = 4.08407044966673

x90 = 10.0530964914873

x91 = -49.9513231920777

x92 = -95.8185759344887

x93 = -43.9822971502571

x94 = -67.8584013175395

x95 = -31.7300858012569

x96 = 98.0176907920015

x97 = -79.7964534011807

x98 = 24.1902634326414

x99 = -47.7522083345649

График