sin6t=1: (уравнение)

Найду корень уравнения: sin6t=1:

Вы ввели

sin(6*t) = 1

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

Подробное решение

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

Быстрый ответ

     pi
t1 = --
     12

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

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

t1 = -83.5140047581305

t2 = 33.7721210833439

t3 = 22.2529479607571

t4 = 99.7455667784648

t5 = 11.7809725139856

t6 = 81.9432084286987

t7 = 0.261799379333194

t8 = 48.4328866713396

t9 = 68.3296401684154

t10 = 15.9697626852522

t11 = 79.8488133554185

t12 = -61.5228561900619

t13 = 84.0376034179138

t14 = -28.012534480777

t15 = -30.1069295278938

t16 = -78.2780169853537

t17 = 94.5095789779178

t18 = -15.4461636998964

t19 = 42.149701543678

t20 = 55.7632696509651

t21 = 44.2440965425203

t22 = 47.3856893488309

t23 = -100.269165531996

t24 = 50.5272818759395

t25 = 2.35619443223801

t26 = -89.797189973996

t27 = 26.4417380971056

t28 = -39.531707620165

t29 = -63.6172513012213

t30 = -45.814892803953

t31 = -12.3045714094311

t32 = -1.8325956303714

t33 = -67.8060413893714

t34 = 37.9609112670449

t35 = 57.8576647795972

t36 = -98.174770348449

t37 = -87.7027949433722

t38 = -56.2868684488565

t39 = 64.1408501103489

t40 = 130.114295757992

t41 = 24.3473430106795

t42 = 6.5449848141863

t43 = 66.2352451246547

t44 = -65.7116463631172

t45 = -23.8237442176309

t46 = 28.5361333386207

t47 = 75.6600230667895

t48 = 92.41518382174

t49 = 77.7544182162793

t50 = 46.3384915894085

t51 = -71.9948316512416

t52 = -34.2957199248261

t53 = 88.2263937072014

t54 = -41.62610272373

t55 = -74.0892266841028

t56 = -76.1836217744616

t57 = -52.0980781057903

t58 = 4.45058952366422

t59 = 70.424035246248

t60 = 90.3207887476935

t61 = -43.7204977825881

t62 = 62.0464548168765

t63 = -37.4373122668668

t64 = 72.5184304232893

t65 = -21.7293492017758

t66 = -10.2101760567131

t67 = -54.1924732011039

t68 = -96.0803752628436

t69 = -6.02138589730989

t70 = 59.9520598481687

t71 = 13.8753675471005

t72 = -58.3812632463393

t73 = 13.8753676266739

t74 = -3.92699098017885

t75 = -93.9859802388653

t76 = -19.6349541459037

t77 = -85.6083998783531

t78 = -32.2013246284748

t79 = -33.2485222538391

t80 = 35.8665162033444

t81 = 18.0641575904069

t82 = -8.11578095040642

t83 = -17.5405590488288

t84 = 40.05530620807

t85 = -50.0036830653347

t86 = -48.9564853809923

t87 = 20.1585529574804

t88 = 9.68657715106654

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