sin6x=0 (уравнение)

Найду корень уравнения: sin6x=0

Вы ввели

sin(6*x) = 0

$$\sin{\left(6 x \right)} = 0$$

Подробное решение

Дано уравнение
$$\sin{\left(6 x \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$\sin{\left(6 x \right)} = 0$$
Это ур-ние преобразуется в
$$6 x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$6 x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Или
$$6 x = 2 \pi n$$
$$6 x = 2 \pi n + \pi$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$6$$
получим ответ:
$$x_{1} = \frac{\pi n}{3}$$
$$x_{2} = \frac{\pi n}{3} + \frac{\pi}{6}$$

Сумма и произведение корней

сумма

        pi
0 + 0 + --
        6 

$$\left(0 + 0\right) + \frac{\pi}{6}$$

=

pi
--
6 

$$\frac{\pi}{6}$$

произведение

    pi
1*0*--
    6 

$$1 \cdot 0 \frac{\pi}{6}$$

=

0

$$0$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     pi
x2 = --
     6 

$$x_{2} = \frac{\pi}{6}$$

Численный ответ

x1 = 36.1283155162826

x2 = -71.733032256967

x3 = 67.5442420521806

x4 = 21.9911485751286

x5 = -31.9395253114962

x6 = -87.9645943005142

x7 = 84.2994028713261

x8 = -90.5825881785057

x9 = 26.1799387799149

x10 = -59.1666616426078

x11 = -43.9822971502571

x12 = -25.6563400043166

x13 = -95.8185759344887

x14 = -85.870199198121

x15 = 48.1710873550435

x16 = 58.1194640914112

x17 = -90.0589894029074

x18 = 6.28318530717959

x19 = 68.0678408277789

x20 = -49.7418836818384

x21 = -34.0339204138894

x22 = 14.1371669411541

x23 = -5.75958653158129

x24 = -75.9218224617533

x25 = 99.4837673636768

x26 = 72.2566310325652

x27 = -12.0427718387609

x28 = 34.0339204138894

x29 = 10.471975511966

x30 = 2.0943951023932

x31 = 62.3082542961976

x32 = 31.9395253114962

x33 = -3.66519142918809

x34 = -21.9911485751286

x35 = 38.2227106186758

x36 = -7.85398163397448

x37 = 93.2005820564972

x38 = 12.0427718387609

x39 = 16.2315620435473

x40 = 82.2050077689329

x41 = 60.2138591938044

x42 = -39.7935069454707

x43 = 34.5575191894877

x44 = -27.7507351067098

x45 = -63.8790506229925

x46 = -97.9129710368819

x47 = -24.0855436775217

x48 = 90.0589894029074

x49 = 53.9306738866248

x50 = 96.342174710087

x51 = 24.0855436775217

x52 = 0.0

x53 = 100.007366139275

x54 = -37.6991118430775

x55 = 65.9734457253857

x56 = -61.7846555205993

x57 = -19.8967534727354

x58 = -41.8879020478639

x59 = -53.9306738866248

x60 = -81.6814089933346

x61 = 28.2743338823081

x62 = -29.845130209103

x63 = -78.0162175641465

x64 = -56.025068989018

x65 = -46.0766922526503

x66 = -82.2050077689329

x67 = 56.025068989018

x68 = 78.0162175641465

x69 = 70.162235930172

x70 = 75.9218224617533

x71 = -93.7241808320955

x72 = -2.0943951023932

x73 = 4.18879020478639

x74 = 40.317105721069

x75 = 97.9129710368819

x76 = 87.9645943005142

x77 = -100.007366139275

x78 = 43.9822971502571

x79 = -17.8023583703422

x80 = 18.3259571459405

x81 = -73.8274273593601

x82 = 94.2477796076938

x83 = -68.0678408277789

x84 = -59.6902604182061

x85 = -51.8362787842316

x86 = -15.707963267949

x87 = 80.1106126665397

x88 = -9.94837673636768

x89 = 9.94837673636768

x90 = 92.1533845053006

x91 = -65.9734457253857

x92 = 50.2654824574367

x93 = -384.84510006475

x94 = 46.0766922526503

x95 = -83.7758040957278

График