sin(4x)=cos(4x) (уравнение)

Найду корень уравнения: sin(4x)=cos(4x)

Вы ввели

sin(4*x) = cos(4*x)

$$\sin{\left(4 x \right)} = \cos{\left(4 x \right)}$$

Подробное решение

Дано уравнение
$$\sin{\left(4 x \right)} = \cos{\left(4 x \right)}$$
преобразуем:
$$\frac{\sin{\left(4 x \right)}}{\cos{\left(4 x \right)}} = 1$$
или
$$\tan{\left(4 x \right)} = 1$$
- 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 = 41.8224522009141

x2 = 19.8313036257856

x3 = 72.4529805734146

x4 = -29.6487806682537

x5 = -21.7947990342792

x6 = 30.0414797499524

x7 = 77.9507677171967

x8 = -17.8678082172919

x9 = 68.5259897564274

x10 = 99.9419162923253

x11 = -53.9961237335746

x12 = -50.0691329165873

x13 = -10.0138265833175

x14 = 4.1233403578366

x15 = -32.004975158446

x16 = 37.8954613839269

x17 = 48.1056375080937

x18 = 98.3711199655304

x19 = -2.15984494934298

x20 = -43.0005494460103

x21 = -24.1509935244715

x22 = -55.5669200603695

x23 = -35.9319659754333

x24 = 18.2605072989907

x25 = -46.1421420996001

x26 = -39.8589567924205

x27 = 58.3158136322605

x28 = -69.7040870015235

x29 = 0.196349540849362

x30 = 55.9596191420682

x31 = -43.7859476094077

x32 = 66.169795266235

x33 = -51.6399292433822

x34 = -99.5492172106266

x35 = -13.9408174003047

x36 = 88.1609438413636

x37 = -28.0779843414588

x38 = 32.3976742401447

x39 = 22.1874981159779

x40 = 33.9684705669396

x41 = 96.0149254753381

x42 = -34.3611696486384

x43 = -61.8501053675491

x44 = 54.3888228152733

x45 = 80.3069622073891

x46 = 36.324665057132

x47 = -79.9142631256904

x48 = 84.2339530243763

x49 = 40.2516558741192

x50 = -63.420901694344

x51 = 76.3799713904018

x52 = -86.1974484328699

x53 = 10.4065256650162

x54 = -11.5846229101124

x55 = 52.0326283250809

x56 = -97.9784208838317

x57 = -90.1244392498572

x58 = 44.1786466911065

x59 = -7.65763209312512

x60 = 51.2472301616835

x61 = -57.9231145505618

x62 = 26.1144889329652

x63 = -95.6222263936393

x64 = 22.9728962793754

x65 = -75.9872723087031

x66 = -65.7770961845363

x67 = 8.05033117482385

x68 = -72.0602814917159

x69 = -3.73064127613788

x70 = 62.2428044492478

x71 = 85.8047493511712

x72 = -91.6952355766521

x73 = -68.1332906747286

x74 = -9.22842841992002

x75 = 63.8136007760427

x76 = -94.0514300668444

x77 = 74.0237769002095

x78 = -77.558068635498

x79 = 92.0879346583508

x80 = -33.5757714852409

x81 = -87.7682447596649

x82 = -35.1465678120358

x83 = 15.9043128087983

x84 = 70.0967860832223

x85 = 59.8866099590554

x86 = 81.877758534184

x87 = 14.3335164820034

x88 = -25.7217898512664

x89 = -73.6310778185108

x90 = -47.712938426395

x91 = -83.8412539426776

x92 = 94.4441291485432

x93 = 11.9773219918111

x94 = -6.08683576633022

График