tg6x=–1 (уравнение)

Найду корень уравнения: tg6x=–1

Вы ввели

tan(6*x) = -1

$$\tan{\left(6 x \right)} = -1$$

Подробное решение

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

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 = -83.9067037896274

x2 = 84.1685031774265

x3 = -64.009950316892

x4 = 98.3056701185806

x5 = -79.717913584841

x6 = -12.1736715326604

x7 = -56.1559686829176

x8 = -91.7606854236019

x9 = -86.0010988920206

x10 = -47.7783882733448

x11 = 67.9369411338793

x12 = -88.0954939944138

x13 = 45.9457925587507

x14 = -1.70169602069447

x15 = -37.8300115369771

x16 = 62.177354602298

x17 = 57.9885643975116

x18 = 40.1862060271694

x19 = 64.2717497046912

x20 = 89.9280897090078

x21 = 50.1345827635371

x22 = -17.9332580642417

x23 = 38.0918109247762

x24 = 53.7997741927252

x25 = 94.1168799137942

x26 = -59.8211601121056

x27 = -10.0792764302673

x28 = 21.860248881229

x29 = -0.130899693899575

x30 = -42.0188017417635

x31 = -81.8123086872342

x32 = 82.0741080750334

x33 = 52.2289778659303

x34 = 60.0829594999048

x35 = -5.89048622548086

x36 = 18.1950574520409

x37 = -54.0615735805244

x38 = -13.7444678594553

x39 = 99.8764664453755

x40 = -20.0276531666349

x41 = 23.9546439836222

x42 = -27.8816348006094

x43 = 6.15228561328001

x44 = -39.9244066393703

x45 = -22.1220482690281

x46 = -78.1471172580461

x47 = -49.872783375738

x48 = -45.6839931709516

x49 = 43.8513974563575

x50 = -35.7356164345839

x51 = 11.9118721448613

x52 = 30.2378292908018

x53 = -69.7695368484733

x54 = 70.0313362362725

x55 = -15.8388629618485

x56 = 79.9797129726402

x57 = 16.1006623496477

x58 = -3.79609112308767

x59 = 1.96349540849362

x60 = 65.8425460314861

x61 = -73.9583270532597

x62 = 9.8174770424681

x63 = 96.2112750161874

x64 = -61.9155552144988

x65 = 26.0490390860154

x66 = 8.24668071567321

x67 = -32.0704250053958

x68 = -76.0527221556529

x69 = 72.1257313386657

x70 = -29.9760299030026

x71 = -7.98488132787406

x72 = 86.2628982798197

x73 = 92.022484811401

x74 = 76.3145215434521

x75 = -98.0438707307815

x76 = -44.1131968441567

x77 = -25.7872396982162

x78 = -57.7267650097125

x79 = -71.8639319508665

x80 = 31.8086256175967

x81 = -93.8550805259951

x82 = 42.2806011295626

x83 = 4.05789051088682

x84 = 87.8336946066146

x85 = -68.1987405216784

x86 = 28.1434341884086

x87 = 14.0062672472545

x88 = -23.692844595823

x89 = 33.9030207199899

x90 = -51.9671784781312

x91 = 48.0401876611439

x92 = 55.8941692951184

x93 = 77.885317870247

x94 = 74.2201264410589

x95 = -66.1043454192852

x96 = 20.2894525544341

x97 = -95.9494756283883

x98 = -34.164820107789

x99 = -90.189889096807

x100 = 35.997415822383

x101 = -100.138265833175

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