tg4x=1 (уравнение)

Найду корень уравнения: tg4x=1

Вы ввели

tan(4*x) = 1

$$\tan{\left(4 x \right)} = 1$$

Подробное решение

Дано уравнение
$$\tan{\left(4 x \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$4 x = \pi n + \operatorname{atan}{\left(1 \right)}$$
Или
$$4 x = \pi n + \frac{\pi}{4}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$4$$
получим ответ:
$$x_{1} = \frac{\pi n}{4} + \frac{\pi}{16}$$

Быстрый ответ

     pi
x1 = --
     16

$$x_{1} = \frac{\pi}{16}$$

Сумма и произведение корней

сумма

    pi
0 + --
    16

$$0 + \frac{\pi}{16}$$

=

pi
--
16

$$\frac{\pi}{16}$$

произведение

  pi
1*--
  16

$$1 \frac{\pi}{16}$$

=

pi
--
16

$$\frac{\pi}{16}$$

Численный ответ

x1 = 72.4529805734146

x2 = 50.4618319982861

x3 = -29.6487806682537

x4 = 60.6720081224529

x5 = -21.7947990342792

x6 = 30.0414797499524

x7 = 77.9507677171967

x8 = -17.8678082172919

x9 = 68.5259897564274

x10 = -45.3567439362026

x11 = 28.4706834231575

x12 = 99.9419162923253

x13 = 86.5901475145687

x14 = -53.9961237335746

x15 = -50.0691329165873

x16 = -10.0138265833175

x17 = 4.1233403578366

x18 = -32.004975158446

x19 = 48.1056375080937

x20 = 98.3711199655304

x21 = -19.4386045440868

x22 = -15.5116137270996

x23 = -55.5669200603695

x24 = -35.9319659754333

x25 = 18.2605072989907

x26 = -27.2925861780613

x27 = -39.8589567924205

x28 = 6.47953484802895

x29 = 58.3158136322605

x30 = -69.7040870015235

x31 = -67.3478925113312

x32 = 0.196349540849362

x33 = 55.9596191420682

x34 = -59.4939108773567

x35 = -23.3655953610741

x36 = -43.7859476094077

x37 = 66.169795266235

x38 = -51.6399292433822

x39 = 90.5171383315559

x40 = -5.30143760293278

x41 = -99.5492172106266

x42 = 20.616701789183

x43 = -37.5027623022282

x44 = -13.9408174003047

x45 = 88.1609438413636

x46 = 32.3976742401447

x47 = 64.5989989394401

x48 = 22.1874981159779

x49 = 33.9684705669396

x50 = 96.0149254753381

x51 = -61.8501053675491

x52 = 54.3888228152733

x53 = 38.6808595473243

x54 = 80.3069622073891

x55 = -85.4120502694725

x56 = 36.324665057132

x57 = -79.9142631256904

x58 = 84.2339530243763

x59 = 40.2516558741192

x60 = -63.420901694344

x61 = 76.3799713904018

x62 = 82.6631566975814

x63 = 10.4065256650162

x64 = -11.5846229101124

x65 = 52.0326283250809

x66 = -97.9784208838317

x67 = 44.1786466911065

x68 = -81.4850594524853

x69 = -7.65763209312512

x70 = -89.3390410864597

x71 = -57.9231145505618

x72 = 26.1144889329652

x73 = -95.6222263936393

x74 = -75.9872723087031

x75 = 42.6078503643116

x76 = -65.7770961845363

x77 = 46.5348411812988

x78 = -72.0602814917159

x79 = 8.05033117482385

x80 = -3.73064127613788

x81 = 62.2428044492478

x82 = -91.6952355766521

x83 = -1.37444678594553

x84 = -41.4297531192154

x85 = -94.0514300668444

x86 = 74.0237769002095

x87 = -77.558068635498

x88 = 2.55254403104171

x89 = 92.0879346583508

x90 = -33.5757714852409

x91 = -87.7682447596649

x92 = 70.0967860832223

x93 = 16.6897109721958

x94 = 14.3335164820034

x95 = -25.7217898512664

x96 = 24.5436926061703

x97 = -73.6310778185108

x98 = -47.712938426395

x99 = -83.8412539426776

x100 = 94.4441291485432

x101 = 11.9773219918111

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