sin12x=0 (уравнение)

Найду корень уравнения: sin12x=0

Вы ввели

sin(12*x) = 0

$$\sin{\left(12 x \right)} = 0$$

Подробное решение

Дано уравнение
$$\sin{\left(12 x \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$\sin{\left(12 x \right)} = 0$$
Это ур-ние преобразуется в
$$12 x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$12 x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Или
$$12 x = 2 \pi n$$
$$12 x = 2 \pi n + \pi$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$12$$
получим ответ:
$$x_{1} = \frac{\pi n}{6}$$
$$x_{2} = \frac{\pi n}{6} + \frac{\pi}{12}$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     pi
x2 = --
     12

$$x_{2} = \frac{\pi}{12}$$

Сумма и произведение корней

сумма

        pi
0 + 0 + --
        12

$$\left(0 + 0\right) + \frac{\pi}{12}$$

=

pi
--
12

$$\frac{\pi}{12}$$

произведение

    pi
1*0*--
    12

$$1 \cdot 0 \frac{\pi}{12}$$

=

0

$$0$$

Численный ответ

x1 = 36.1283155162826

x2 = -71.733032256967

x3 = -23.8237442897226

x4 = 71.733032256967

x5 = -11.7809724509617

x6 = -54.1924732744239

x7 = 8.11578102177363

x8 = -3.92699081698724

x9 = -43.720497762458

x10 = 52.0980781720307

x11 = -21.7293491873294

x12 = 26.1799387799149

x13 = -95.8185759344887

x14 = -69.9004365423729

x15 = -85.870199198121

x16 = -33.7721210260903

x17 = -32.4631240870945

x18 = 48.1710873550435

x19 = 58.1194640914112

x20 = 6.28318530717959

x21 = -47.9092879672443

x22 = 14.1371669411541

x23 = -5.75958653158129

x24 = -75.9218224617533

x25 = -50.0036830696375

x26 = 2.0943951023932

x27 = 22.2529479629277

x28 = -87.4409955249159

x29 = 38.2227106186758

x30 = 86.1319985859202

x31 = -7.85398163397448

x32 = 42.1497014356631

x33 = -77.7544181763474

x34 = -65.7116463375865

x35 = 32.2013246992954

x36 = 100.269165527074

x37 = 10.2101761241668

x38 = -25.9181393921158

x39 = 88.2263936883134

x40 = 16.2315620435473

x41 = 82.2050077689329

x42 = -91.8915851175014

x43 = -1.83259571459405

x44 = 60.2138591938044

x45 = -39.7935069454707

x46 = 67.8060414399797

x47 = 34.5575191894877

x48 = -55.7632696012188

x49 = -27.7507351067098

x50 = -63.8790506229925

x51 = -97.9129710368819

x52 = 44.2440965380563

x53 = 90.0589894029074

x54 = 64.1408500107916

x55 = 24.0855436775217

x56 = 0.0

x57 = 74.0892267471593

x58 = 78.2780169519457

x59 = 66.2352451131848

x60 = 56.2868683768171

x61 = -36.6519142918809

x62 = -61.7846555205993

x63 = -19.8967534727354

x64 = -41.8879020478639

x65 = -21.4675497995303

x66 = 28.2743338823081

x67 = -29.845130209103

x68 = 96.0803753222878

x69 = 70.162235930172

x70 = 30.1069295969022

x71 = -93.7241808320955

x72 = 63.093652459595

x73 = 4.18879020478639

x74 = -57.857664703612

x75 = 98.174770424681

x76 = 20.1585528605345

x77 = -89.7971900151083

x78 = -45.8148928648512

x79 = -17.8023583703422

x80 = -73.8274273593601

x81 = 94.2477796076938

x82 = -661.567052968451

x83 = -51.8362787842316

x84 = -15.707963267949

x85 = 80.1106126665397

x86 = -67.8060414399797

x87 = 54.1924732744239

x88 = 78.5398163397448

x89 = 76.1836218495525

x90 = 92.1533845053006

x91 = 50.2654824574367

x92 = -35.8665161284835

x93 = -99.7455667514759

x94 = 46.0766922526503

x95 = -79.8488132787406

x96 = -13.8753675533549

x97 = -83.7758040957278

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