tg8x=1 (уравнение)

Найду корень уравнения: tg8x=1

Вы ввели

tan(8*x) = 1

$$\tan{\left(8 x \right)} = 1$$

Подробное решение

Дано уравнение
$$\tan{\left(8 x \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$8 x = \pi n + \operatorname{atan}{\left(1 \right)}$$
Или
$$8 x = \pi n + \frac{\pi}{4}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$8$$
получим ответ:
$$x_{1} = \frac{\pi n}{8} + \frac{\pi}{32}$$

Быстрый ответ

     pi
x1 = --
     32

$$x_{1} = \frac{\pi}{32}$$

Сумма и произведение корней

сумма

    pi
0 + --
    32

$$0 + \frac{\pi}{32}$$

=

pi
--
32

$$\frac{\pi}{32}$$

произведение

  pi
1*--
  32

$$1 \frac{\pi}{32}$$

=

pi
--
32

$$\frac{\pi}{32}$$

Численный ответ

x1 = 41.3315783487907

x2 = -18.7513811511141

x3 = 37.0118884501047

x4 = -7.7558068635498

x5 = -13.6462930890307

x6 = -3.82881604656256

x7 = -41.1352288079414

x8 = -23.8564692131975

x9 = -55.6650948307941

x10 = -73.7292525889355

x11 = -469.177227859551

x12 = 76.2817966199772

x13 = 36.2264902867073

x14 = 40.1534811036945

x15 = 14.2353417115787

x16 = 44.0804719206818

x17 = 4.81056375080937

x18 = 28.3725086527328

x19 = 52.327152636355

x20 = 8.34485548609789

x21 = -69.8022617719482

x22 = 71.5694076395925

x23 = -31.710450847172

x24 = 48.007462737669

x25 = -16.002487579223

x26 = -35.6374416641592

x27 = 85.7065745807465

x28 = -33.6739462556656

x29 = 56.2541434533422

x30 = -91.7934103470768

x31 = -67.8387663634546

x32 = 6.38136007760427

x33 = -79.6197388144163

x34 = -71.7657571804418

x35 = 41.7242774304894

x36 = -66.2679700366597

x37 = -27.7834600301847

x38 = 96.3094497866121

x39 = -43.8841223798324

x40 = -59.9847847294801

x41 = -76.4781461608265

x42 = -89.8299149385831

x43 = -75.6927479974291

x44 = 72.3548058029899

x45 = 30.3360040612264

x46 = 12.2718463030851

x47 = 69.9986113127976

x48 = 38.1899856952009

x49 = -1.86532063806894

x50 = -87.0810213666921

x51 = 58.2176388618359

x52 = -11.682797680537

x53 = 95.5240516232146

x54 = 54.2906480448486

x55 = -83.1540305497048

x56 = 98.2729451951057

x57 = 62.1446296788231

x58 = -49.7746086053133

x59 = -77.6562434059227

x60 = 34.2629948782137

x61 = -45.847617788326

x62 = 82.172282845458

x63 = 84.1357782539517

x64 = 63.715426005618

x65 = -87.8664195300895

x66 = 91.9897598879261

x67 = -14.4316912524281

x68 = 60.1811342703295

x69 = -37.9936361543516

x70 = -29.7469554386784

x71 = -97.6838965725576

x72 = -93.7569057555704

x73 = -1.07992247467149

x74 = 32.2994994697201

x75 = 16.1988371200724

x76 = 80.2087874369644

x77 = -53.7015994223005

x78 = -57.6285902392878

x79 = 74.3183012114835

x80 = 86.8846718258427

x81 = -5.79231145505618

x82 = -22.6783719681013

x83 = -99.6473919810513

x84 = 94.3459543781185

x85 = 78.2452920284708

x86 = 50.3636572278614

x87 = 10.3083508945915

x88 = -51.7381040138069

x89 = -25.8199646216911

x90 = 19.7331288553609

x91 = -47.8111131968197

x92 = 18.9477306919634

x93 = 18.162332528566

x94 = -63.5190764647686

x95 = -95.720401164064

x96 = -9.71930227204342

x97 = 26.0163141625405

x98 = 100.236440603599

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