sin6x=1 (уравнение)

Найду корень уравнения: sin6x=1

Вы ввели

sin(6*x) = 1

$$\sin{\left(6 x \right)} = 1$$

Подробное решение

Дано уравнение
$$\sin{\left(6 x \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$6 x = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$6 x = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Или
$$6 x = 2 \pi n + \frac{\pi}{2}$$
$$6 x = 2 \pi n + \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$6$$
получим ответ:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{12}$$
$$x_{2} = \frac{\pi n}{3} + \frac{\pi}{12}$$

Быстрый ответ

     pi
x1 = --
     12

$$x_{1} = \frac{\pi}{12}$$

Сумма и произведение корней

сумма

    pi
0 + --
    12

$$0 + \frac{\pi}{12}$$

=

pi
--
12

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

произведение

  pi
1*--
  12

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

=

pi
--
12

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

Численный ответ

x1 = -28.012534480777

x2 = 57.8576647795972

x3 = -41.62610272373

x4 = 22.2529479607571

x5 = -85.6083998783531

x6 = -50.0036830653347

x7 = 42.149701543678

x8 = -1.8325956303714

x9 = 37.9609112670449

x10 = -48.9564853809923

x11 = 35.8665162033444

x12 = -3.92699098017885

x13 = -19.6349541459037

x14 = 20.1585529574804

x15 = -71.9948316512416

x16 = 40.05530620807

x17 = -67.8060413893714

x18 = -30.1069295278938

x19 = 2.35619443223801

x20 = 79.8488133554185

x21 = -52.0980781057903

x22 = 130.114295757992

x23 = -33.2485222538391

x24 = -39.531707620165

x25 = -83.5140047581305

x26 = 11.7809725139856

x27 = -61.5228561900619

x28 = 50.5272818759395

x29 = -17.5405590488288

x30 = 55.7632696509651

x31 = -6.02138589730989

x32 = 24.3473430106795

x33 = -63.6172513012213

x34 = 92.41518382174

x35 = 64.1408501103489

x36 = -12.3045714094311

x37 = 68.3296401684154

x38 = 59.9520598481687

x39 = -43.7204977825881

x40 = -74.0892266841028

x41 = 9.68657715106654

x42 = 6.5449848141863

x43 = 88.2263937072014

x44 = 44.2440965425203

x45 = 90.3207887476935

x46 = 70.424035246248

x47 = -15.4461636998964

x48 = 18.0641575904069

x49 = -45.814892803953

x50 = -89.797189973996

x51 = 28.5361333386207

x52 = -54.1924732011039

x53 = 13.8753675471005

x54 = -10.2101760567131

x55 = 46.3384915894085

x56 = -23.8237442176309

x57 = 77.7544182162793

x58 = -21.7293492017758

x59 = 75.6600230667895

x60 = -87.7027949433722

x61 = 81.9432084286987

x62 = 0.261799379333194

x63 = 33.7721210833439

x64 = 13.8753676266739

x65 = -96.0803752628436

x66 = 48.4328866713396

x67 = 47.3856893488309

x68 = -78.2780169853537

x69 = 66.2352451246547

x70 = -76.1836217744616

x71 = -65.7116463631172

x72 = 26.4417380971056

x73 = 62.0464548168765

x74 = -8.11578095040642

x75 = -37.4373122668668

x76 = 15.9697626852522

x77 = -32.2013246284748

x78 = 4.45058952366422

x79 = -98.174770348449

x80 = 72.5184304232893

x81 = -56.2868684488565

x82 = -34.2957199248261

x83 = -100.269165531996

x84 = 99.7455667784648

x85 = -58.3812632463393

x86 = -93.9859802388653

x87 = 94.5095789779178

x88 = 84.0376034179138

График