tg(5x-2)=-√3 (уравнение)

Найду корень уравнения: tg(5x-2)=-√3

Вы ввели

                  ___
tan(5*x - 2) = -\/ 3 

$$\tan{\left(5 x - 2 \right)} = - \sqrt{3}$$

Подробное решение

Дано уравнение
$$\tan{\left(5 x - 2 \right)} = - \sqrt{3}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$5 x - 2 = \pi n + \operatorname{atan}{\left(- \sqrt{3} \right)}$$
Или
$$5 x - 2 = \pi n - \frac{\pi}{3}$$
, где n - любое целое число
Перенесём
$$-2$$
в правую часть ур-ния
с противоположным знаком, итого:
$$5 x = \pi n - \frac{\pi}{3} + 2$$
Разделим обе части полученного ур-ния на
$$5$$
получим ответ:
$$x_{1} = \frac{\pi n}{5} - \frac{\pi}{15} + \frac{2}{5}$$

Быстрый ответ

     2   pi
x1 = - - --
     5   15

$$x_{1} = \frac{2}{5} - \frac{\pi}{15}$$

Сумма и произведение корней

сумма

    2   pi
0 + - - --
    5   15

$$0 + \left(\frac{2}{5} - \frac{\pi}{15}\right)$$

=

2   pi
- - --
5   15

$$\frac{2}{5} - \frac{\pi}{15}$$

произведение

  /2   pi\
1*|- - --|
  \5   15/

$$1 \cdot \left(\frac{2}{5} - \frac{\pi}{15}\right)$$

=

2   pi
- - --
5   15

$$\frac{2}{5} - \frac{\pi}{15}$$

Численный ответ

x1 = -95.942174710087

x2 = 0.19056048976068

x3 = -7.97758040957278

x4 = 98.2082512817622

x5 = -85.8890782185996

x6 = 25.951620249197

x7 = 24.0666646570431

x8 = -48.1899663755221

x9 = 88.1551547902749

x10 = 10.243656981248

x11 = 61.7657765001206

x12 = 38.5179908635562

x13 = -87.7740338107535

x14 = 91.9250659745826

x15 = 36.0047167406843

x16 = 90.0401103824288

x17 = -26.1988178003936

x18 = 17.7834793498635

x19 = 2.07551608191456

x20 = -77.7209373192662

x21 = -60.1280184591633

x22 = -31.8536845768552

x23 = 100.093206873916

x24 = 49.8277244164794

x25 = 46.0578132321717

x26 = 56.110909723659

x27 = -80.234211442138

x28 = 59.8808209079668

x29 = 76.2171027066337

x30 = -24.3138622082397

x31 = -28.0837733925475

x32 = -90.2873079336254

x33 = 93.8100215667365

x34 = -53.8448331519838

x35 = 3.96047167406843

x36 = -92.1722635257792

x37 = 57.9958653158129

x38 = 32.2348055563766

x39 = -38.1368698840348

x40 = -99.7120858943947

x41 = -73.9510261349584

x42 = 54.2259541315051

x43 = -18.0306769010601

x44 = -40.0218254761887

x45 = -84.0041226264458

x46 = -68.2961593584968

x47 = -19.915632493214

x48 = 51.7126800086333

x49 = -82.1191670342919

x50 = 79.9870138909414

x51 = 68.0489618073002

x52 = 71.818872991608

x53 = -75.8359817271123

x54 = -6.09262481741891

x55 = 20.2967534727354

x56 = -43.7917366604964

x57 = -16.1457213089062

x58 = -11.7474915938805

x59 = -94.0572191179331

x60 = -70.1811149506507

x61 = 64.2790506229925

x62 = 22.1817090648892

x63 = 34.1197611485305

x64 = -63.8979296434711

x65 = -55.7297887441376

x66 = -29.9687289847013

x67 = 14.0135681655558

x68 = 95.6949771588904

x69 = 44.1728576400178

x70 = -4.20766922526503

x71 = 5.84542726622231

x72 = -58.2430628670095

x73 = -65.782885235625

x74 = -9.86253600172666

x75 = 69.9339173994541

x76 = -33.7386401690091

x77 = -62.0129740513172

x78 = -97.8271303022409

x79 = -14.2607657167524

x80 = 73.7038285837618

x81 = 7.73038285837618

x82 = 83.7569250752492

x83 = 29.7215314335047

x84 = -21.8005880853679

x85 = -36.2519142918809

x86 = -2.32271363311115

x87 = 86.270199198121

x88 = 27.8365758413509

x89 = -41.9067810683425

x90 = 47.9427688243255

x91 = 81.8719694830953

x92 = 78.1020582987876

x93 = -46.3050107833683

x94 = 66.1640062151463

x95 = -50.074921967676

x96 = 39.7746279249921

x97 = -51.9598775598299

x98 = 42.2879020478639

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