sin(6x)=0 (уравнение)

Найду корень уравнения: sin(6x)=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:
$$x_{1} = \frac{\pi n}{3}$$
$$x_{2} = \frac{\pi n}{3} + \frac{\pi}{6}$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     pi
x2 = --
     6 

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

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

$$0$$

Численный ответ

x1 = 48.1710873550435

x2 = 40.317105721069

x3 = 50.2654824574367

x4 = -3.66519142918809

x5 = 90.0589894029074

x6 = 26.1799387799149

x7 = 36.1283155162826

x8 = -7.85398163397448

x9 = -73.8274273593601

x10 = -65.9734457253857

x11 = 87.9645943005142

x12 = -37.6991118430775

x13 = 84.2994028713261

x14 = -21.9911485751286

x15 = -93.7241808320955

x16 = 82.2050077689329

x17 = -83.7758040957278

x18 = 92.1533845053006

x19 = -46.0766922526503

x20 = 2.0943951023932

x21 = -53.9306738866248

x22 = -34.0339204138894

x23 = 28.2743338823081

x24 = -384.84510006475

x25 = -17.8023583703422

x26 = 10.471975511966

x27 = -15.707963267949

x28 = -12.0427718387609

x29 = -56.025068989018

x30 = -27.7507351067098

x31 = -51.8362787842316

x32 = -31.9395253114962

x33 = 53.9306738866248

x34 = 65.9734457253857

x35 = 62.3082542961976

x36 = 18.3259571459405

x37 = 14.1371669411541

x38 = -78.0162175641465

x39 = -61.7846555205993

x40 = 68.0678408277789

x41 = -59.1666616426078

x42 = 72.2566310325652

x43 = -19.8967534727354

x44 = 4.18879020478639

x45 = 34.0339204138894

x46 = 0.0

x47 = 43.9822971502571

x48 = -71.733032256967

x49 = -85.870199198121

x50 = 80.1106126665397

x51 = 78.0162175641465

x52 = 21.9911485751286

x53 = -25.6563400043166

x54 = -43.9822971502571

x55 = 46.0766922526503

x56 = 58.1194640914112

x57 = -97.9129710368819

x58 = -82.2050077689329

x59 = 60.2138591938044

x60 = -39.7935069454707

x61 = 99.4837673636768

x62 = 100.007366139275

x63 = 67.5442420521806

x64 = 97.9129710368819

x65 = 6.28318530717959

x66 = -5.75958653158129

x67 = 34.5575191894877

x68 = 56.025068989018

x69 = -100.007366139275

x70 = 96.342174710087

x71 = 9.94837673636768

x72 = -95.8185759344887

x73 = 31.9395253114962

x74 = -90.0589894029074

x75 = 93.2005820564972

x76 = 75.9218224617533

x77 = -59.6902604182061

x78 = -49.7418836818384

x79 = 12.0427718387609

x80 = -63.8790506229925

x81 = 38.2227106186758

x82 = 70.162235930172

x83 = 24.0855436775217

x84 = -68.0678408277789

x85 = -87.9645943005142

x86 = -75.9218224617533

x87 = -24.0855436775217

x88 = -90.5825881785057

x89 = -29.845130209103

x90 = -41.8879020478639

x91 = -2.0943951023932

x92 = 16.2315620435473

x93 = 94.2477796076938

x94 = -81.6814089933346

x95 = -9.94837673636768

График