tan4x=1 (уравнение)

Найду корень уравнения: tan4x=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 = -41.4297531192154

x2 = 70.0967860832223

x3 = -81.4850594524853

x4 = 4.1233403578366

x5 = -69.7040870015235

x6 = 2.55254403104171

x7 = -37.5027623022282

x8 = 68.5259897564274

x9 = -53.9961237335746

x10 = 58.3158136322605

x11 = 36.324665057132

x12 = -65.7770961845363

x13 = -3.73064127613788

x14 = -27.2925861780613

x15 = -43.7859476094077

x16 = 6.47953484802895

x17 = -63.420901694344

x18 = 18.2605072989907

x19 = -33.5757714852409

x20 = 88.1609438413636

x21 = -55.5669200603695

x22 = -1.37444678594553

x23 = 52.0326283250809

x24 = 99.9419162923253

x25 = -83.8412539426776

x26 = -57.9231145505618

x27 = 48.1056375080937

x28 = -32.004975158446

x29 = -77.558068635498

x30 = -91.6952355766521

x31 = -10.0138265833175

x32 = -67.3478925113312

x33 = 24.5436926061703

x34 = -47.712938426395

x35 = -45.3567439362026

x36 = -35.9319659754333

x37 = 76.3799713904018

x38 = -95.6222263936393

x39 = -13.9408174003047

x40 = -11.5846229101124

x41 = -59.4939108773567

x42 = 80.3069622073891

x43 = -89.3390410864597

x44 = -29.6487806682537

x45 = -17.8678082172919

x46 = -85.4120502694725

x47 = 92.0879346583508

x48 = 50.4618319982861

x49 = 64.5989989394401

x50 = 11.9773219918111

x51 = 90.5171383315559

x52 = -51.6399292433822

x53 = 72.4529805734146

x54 = -79.9142631256904

x55 = 44.1786466911065

x56 = 30.0414797499524

x57 = -39.8589567924205

x58 = -72.0602814917159

x59 = -94.0514300668444

x60 = 40.2516558741192

x61 = 16.6897109721958

x62 = -23.3655953610741

x63 = -87.7682447596649

x64 = -97.9784208838317

x65 = 77.9507677171967

x66 = -61.8501053675491

x67 = -25.7217898512664

x68 = 55.9596191420682

x69 = -75.9872723087031

x70 = 0.196349540849362

x71 = 38.6808595473243

x72 = 10.4065256650162

x73 = 33.9684705669396

x74 = 74.0237769002095

x75 = 42.6078503643116

x76 = 94.4441291485432

x77 = 46.5348411812988

x78 = 20.616701789183

x79 = 62.2428044492478

x80 = -73.6310778185108

x81 = 28.4706834231575

x82 = -15.5116137270996

x83 = -50.0691329165873

x84 = 14.3335164820034

x85 = -5.30143760293278

x86 = 98.3711199655304

x87 = 84.2339530243763

x88 = 86.5901475145687

x89 = -99.5492172106266

x90 = 60.6720081224529

x91 = -7.65763209312512

x92 = 96.0149254753381

x93 = -19.4386045440868

x94 = -21.7947990342792

x95 = 66.169795266235

x96 = 54.3888228152733

x97 = 82.6631566975814

x98 = 8.05033117482385

x99 = 22.1874981159779

x100 = 32.3976742401447

x101 = 26.1144889329652

График