tg(-4x)=1/√3 (уравнение)

Найду корень уравнения: tg(-4x)=1/√3

Вы ввели

                1  
tan(-4*x) = 1*-----
                ___
              \/ 3 

$$\tan{\left(- 4 x \right)} = 1 \cdot \frac{1}{\sqrt{3}}$$

Подробное решение

Дано уравнение
$$\tan{\left(- 4 x \right)} = 1 \cdot \frac{1}{\sqrt{3}}$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на -1

Ур-ние превратится в
$$\tan{\left(4 x \right)} = - \frac{\sqrt{3}}{3}$$
Это ур-ние преобразуется в
$$4 x = \pi n + \operatorname{atan}{\left(- \frac{\sqrt{3}}{3} \right)}$$
Или
$$4 x = \pi n - \frac{\pi}{6}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$4$$
получим ответ:
$$x_{1} = \frac{\pi n}{4} - \frac{\pi}{24}$$

Быстрый ответ

     -pi 
x1 = ----
      24 

$$x_{1} = - \frac{\pi}{24}$$

Сумма и произведение корней

сумма

    pi
0 - --
    24

$$- \frac{\pi}{24} + 0$$

=

-pi 
----
 24 

$$- \frac{\pi}{24}$$

произведение

  -pi 
1*----
   24 

$$1 \left(- \frac{\pi}{24}\right)$$

=

-pi 
----
 24 

$$- \frac{\pi}{24}$$

Численный ответ

x1 = -4.05789051088682

x2 = 60.3447588877039

x3 = -33.9030207199899

x4 = -41.7570023539643

x5 = 68.1987405216784

x6 = 11.6500727570621

x7 = 95.6876762405891

x8 = 7.72308194007491

x9 = 69.7695368484733

x10 = -88.0954939944138

x11 = 73.6965276654606

x12 = -85.7392995042214

x13 = -1.70169602069447

x14 = -37.8300115369771

x15 = 57.9885643975116

x16 = -49.6109839879388

x17 = -70.0313362362725

x18 = 64.2717497046912

x19 = 50.1345827635371

x20 = 94.1168799137942

x21 = 90.189889096807

x22 = -59.8211601121056

x23 = 61.9155552144988

x24 = 21.860248881229

x25 = 98.0438707307815

x26 = -0.130899693899575

x27 = 78.4089166458453

x28 = -77.885317870247

x29 = -81.8123086872342

x30 = -92.022484811401

x31 = -71.6021325630674

x32 = -54.3233729683235

x33 = -26.0490390860154

x34 = -89.6662903212087

x35 = -27.6198354128103

x36 = 24.2164433714213

x37 = 6.15228561328001

x38 = -62.177354602298

x39 = -22.1220482690281

x40 = -55.8941692951184

x41 = -11.9118721448613

x42 = -63.7481509290929

x43 = 91.7606854236019

x44 = -45.6839931709516

x45 = 43.8513974563575

x46 = 29.7142305152035

x47 = -98.3056701185806

x48 = 100.400065220974

x49 = -84.1685031774265

x50 = -15.8388629618485

x51 = 79.9797129726402

x52 = -48.0401876611439

x53 = -32.332224393195

x54 = 46.2075919465499

x55 = 65.8425460314861

x56 = -73.9583270532597

x57 = -76.3145215434521

x58 = -14.2680666350536

x59 = -18.1950574520409

x60 = 34.4266194955881

x61 = -80.2415123604393

x62 = 10.0792764302673

x63 = 72.1257313386657

x64 = -29.9760299030026

x65 = -5.62868683768171

x66 = -7.98488132787406

x67 = -93.5932811381959

x68 = 51.705379090332

x69 = -99.8764664453755

x70 = 86.2628982798197

x71 = 56.4177680707167

x72 = 17.9332580642417

x73 = 3.79609112308767

x74 = 25.7872396982162

x75 = -44.1131968441567

x76 = -40.1862060271694

x77 = 83.9067037896274

x78 = 32.0704250053958

x79 = 42.2806011295626

x80 = -58.2503637853107

x81 = 87.8336946066146

x82 = -36.2592152101822

x83 = 47.7783882733448

x84 = 39.9244066393703

x85 = 28.1434341884086

x86 = 14.0062672472545

x87 = 76.0527221556529

x88 = -23.692844595823

x89 = 54.0615735805244

x90 = -51.9671784781312

x91 = -67.6751417460801

x92 = -10.3410758180664

x93 = 16.3624617374468

x94 = 38.3536103125754

x95 = -19.7658537788358

x96 = -66.1043454192852

x97 = 20.2894525544341

x98 = -95.9494756283883

x99 = 2.22529479629277

x100 = 35.997415822383

x101 = 82.3359074628325

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