sin(3x)=cos(3x) (уравнение)

Найду корень уравнения: sin(3x)=cos(3x)

Вы ввели

sin(3*x) = cos(3*x)

$$\sin{\left(3 x \right)} = \cos{\left(3 x \right)}$$

Подробное решение

Дано уравнение
$$\sin{\left(3 x \right)} = \cos{\left(3 x \right)}$$
преобразуем:
$$\frac{\sin{\left(3 x \right)}}{\cos{\left(3 x \right)}} = 1$$
или
$$\tan{\left(3 x \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$3 x = \pi n + \operatorname{atan}{\left(-1 \right)}$$
Или
$$3 x = \pi n - \frac{\pi}{4}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = \frac{\pi n}{3} - \frac{\pi}{12}$$

Быстрый ответ

     pi
x1 = --
     12

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

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

x1 = 24.3473430653209

x2 = 215.984494934298

x3 = -39.5317075576716

x4 = -23.8237442897226

x5 = 57.857664703612

x6 = 68.329640215578

x7 = -10.2101761241668

x8 = -54.1924732744239

x9 = -78.2780169519457

x10 = 26.4417381677141

x11 = -3.92699081698724

x12 = 71.4712328691678

x13 = -63.6172512351933

x14 = 52.621676947629

x15 = -43.720497762458

x16 = -100.269165527074

x17 = -34.2957198016886

x18 = -21.7293491873294

x19 = 50.5272818452358

x20 = -28.012534494509

x21 = -69.9004365423729

x22 = 48.4328867428426

x23 = -47.9092879672443

x24 = 92.4151838930998

x25 = 10.7337748997651

x26 = 4.45058959258554

x27 = -50.0036830696375

x28 = 0.261799387799149

x29 = 55.7632696012188

x30 = 11.7809724509617

x31 = 22.2529479629277

x32 = -52.0980781720307

x33 = 86.1319985859202

x34 = -15.4461638801498

x35 = 18.0641577581413

x36 = 42.1497014356631

x37 = -83.5140047079287

x38 = 30.6305283725005

x39 = -1053.21893711598

x40 = -65.7116463375865

x41 = 13.8753675533549

x42 = -96.0803753222878

x43 = 40.0553063332699

x44 = -17.540558982543

x45 = -25.9181393921158

x46 = 59.9520598060052

x47 = -74.0892267471593

x48 = 88.2263936883134

x49 = -91.8915851175014

x50 = -1.83259571459405

x51 = -41.6261026600648

x52 = 35.8665161284835

x53 = 28.5361332701073

x54 = 44.2440965380563

x55 = 75.6600230739542

x56 = -71.9948316447661

x57 = -12.30457122656

x58 = -32.2013246992954

x59 = -30.1069295969022

x60 = -6.02138591938044

x61 = 49.4800842940392

x62 = 2.35619449019234

x63 = -85.6083998103219

x64 = 64.1408500107916

x65 = 72.5184304203644

x66 = 90.3207887907066

x67 = 66.2352451131848

x68 = 94.5095789954929

x69 = 46.3384916404494

x70 = 15.9697626557481

x71 = 101.839961853869

x72 = 79.8488132787406

x73 = 70.4240353179712

x74 = 84.037603483527

x75 = -58.3812634792103

x76 = 99.7455667514759

x77 = 62.0464549083984

x78 = -76.1836218495525

x79 = -93.9859802198946

x80 = 20.1585528605345

x81 = -89.7971900151083

x82 = -8.11578102177363

x83 = -56.2868683768171

x84 = -45.8148928648512

x85 = -80.3724120543389

x86 = 81.9432083811338

x87 = 77.7544181763474

x88 = -61.5228561328001

x89 = 37.9609112308767

x90 = -67.8060414399797

x91 = 6.54498469497874

x92 = -98.174770424681

x93 = 33.7721210260903

x94 = -87.7027949127151

x95 = -19.6349540849362

x96 = 2287.34125120117

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