tg5x=√3 (уравнение)

Найду корень уравнения: tg5x=√3

Вы ввели

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tan(5*x) = \/ 3 

$$\tan{\left(5 x \right)} = \sqrt{3}$$

Подробное решение

Дано уравнение
$$\tan{\left(5 x \right)} = \sqrt{3}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$5 x = \pi n + \operatorname{atan}{\left(\sqrt{3} \right)}$$
Или
$$5 x = \pi n + \frac{\pi}{3}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$5$$
получим ответ:
$$x_{1} = \frac{\pi n}{5} + \frac{\pi}{15}$$

Быстрый ответ

     pi
x1 = --
     15

$$x_{1} = \frac{\pi}{15}$$

Сумма и произведение корней

сумма

    pi
0 + --
    15

$$0 + \frac{\pi}{15}$$

=

pi
--
15

$$\frac{\pi}{15}$$

произведение

  pi
1*--
  15

$$1 \frac{\pi}{15}$$

=

pi
--
15

$$\frac{\pi}{15}$$

Численный ответ

x1 = -1.67551608191456

x2 = -67.6489618073002

x3 = -47.5427688243255

x4 = -55.710909723659

x5 = 90.0589894029074

x6 = -33.7197611485304

x7 = -15.4985237577096

x8 = 48.5899663755221

x9 = 42.3067810683426

x10 = 66.182885235625

x11 = -43.7728576400178

x12 = 38.5368698840348

x13 = 34.1386401690091

x14 = 50.474921967676

x15 = -45.6578132321717

x16 = -73.9321471144798

x17 = -23.6666646570431

x18 = -61.9940950308386

x19 = 22.2005880853679

x20 = -21.7817090648892

x21 = 44.1917366604964

x22 = 2.0943951023932

x23 = 78.1209373192662

x24 = 54.2448331519838

x25 = 26.5988178003936

x26 = 98.2271303022409

x27 = -71.418872991608

x28 = 70.5811149506507

x29 = 8.37758040957278

x30 = -40.00294645571

x31 = 30.3687289847013

x32 = -89.6401103824288

x33 = 72.4660705428046

x34 = -5.44542726622231

x35 = -49.4277244164794

x36 = -69.5339173994541

x37 = 86.2890782185997

x38 = 88.1740338107535

x39 = -99.6932068739161

x40 = -87.7551547902749

x41 = -3.56047167406843

x42 = 58.0147443362915

x43 = 28.4837733925475

x44 = 80.0058929114201

x45 = -93.4100215667365

x46 = 68.0678408277789

x47 = 40.4218254761887

x48 = 62.4129740513172

x49 = -57.5958653158129

x50 = 20.315632493214

x51 = -95.9232956896084

x52 = 36.023595761163

x53 = -27.4365758413509

x54 = 60.5280184591633

x55 = -79.5870138909414

x56 = -19.8967534727354

x57 = -85.870199198121

x58 = 74.3510261349584

x59 = 100.112085894395

x60 = 32.2536845768552

x61 = 52.3598775598299

x62 = -7.95870138909414

x63 = -37.4896723328382

x64 = 46.0766922526503

x65 = -81.4719694830953

x66 = -65.7640062151463

x67 = -18.0117978805815

x68 = 0.20943951023932

x69 = 76.2359817271123

x70 = 82.5191670342919

x71 = -97.8082512817622

x72 = -11.7286125734019

x73 = 16.5457213089062

x74 = 84.4041226264458

x75 = 4.60766922526503

x76 = -29.9498499642227

x77 = 56.1297887441376

x78 = -83.9852436059671

x79 = 92.5722635257792

x80 = 6.49262481741891

x81 = -13.6135681655558

x82 = 14.0324471860344

x83 = 10.2625360017267

x84 = 96.342174710087

x85 = -77.7020582987875

x86 = 64.2979296434711

x87 = -31.8348055563766

x88 = -53.8259541315051

x89 = -63.8790506229925

x90 = 18.4306769010601

x91 = -75.8171027066337

x92 = 24.0855436775217

x93 = -35.6047167406843

x94 = 94.4572191179331

x95 = -51.9409985393512

x96 = -25.551620249197

x97 = -9.84365698124802

x98 = -91.5250659745826

x99 = -41.8879020478639

x100 = 12.1474915938805

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