tg(2x-3)=-1 (уравнение)

Найду корень уравнения: tg(2x-3)=-1

Вы ввели

tan(2*x - 3) = -1

$$\tan{\left(2 x - 3 \right)} = -1$$

Подробное решение

Дано уравнение
$$\tan{\left(2 x - 3 \right)} = -1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$2 x - 3 = \pi n + \operatorname{atan}{\left(-1 \right)}$$
Или
$$2 x - 3 = \pi n - \frac{\pi}{4}$$
, где n - любое целое число
Перенесём
$$-3$$
в правую часть ур-ния
с противоположным знаком, итого:
$$2 x = \pi n - \frac{\pi}{4} + 3$$
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = \frac{\pi n}{2} - \frac{\pi}{8} + \frac{3}{2}$$

Быстрый ответ

     3   pi
x1 = - - --
     2   8 

$$x_{1} = \frac{3}{2} - \frac{\pi}{8}$$

Сумма и произведение корней

сумма

    3   pi
0 + - - --
    2   8 

$$0 + \left(\frac{3}{2} - \frac{\pi}{8}\right)$$

=

3   pi
- - --
2   8 

$$\frac{3}{2} - \frac{\pi}{8}$$

произведение

  /3   pi\
1*|- - --|
  \2   8 /

$$1 \cdot \left(\frac{3}{2} - \frac{\pi}{8}\right)$$

=

3   pi
- - --
2   8 

$$\frac{3}{2} - \frac{\pi}{8}$$

Численный ответ

x1 = 51.372783375738

x2 = 93.7842841992002

x3 = -83.7157007286231

x4 = -11.4590696960579

x5 = -97.8528676697772

x6 = -8.3174770424681

x7 = 59.2267650097125

x8 = 54.5143760293278

x9 = -44.4457925587507

x10 = 49.8019870489431

x11 = 56.0851723561227

x12 = -72.7201264410589

x13 = 45.0895980685584

x14 = 79.6471172580461

x15 = -100.994460323367

x16 = 35.664820107789

x17 = 76.5055246044563

x18 = 85.9303025652257

x19 = -52.2997741927252

x20 = -69.5785337874691

x21 = 71.7931356240716

x22 = -47.5873852123405

x23 = 21.5276531666349

x24 = 95.3550805259951

x25 = 37.2356164345839

x26 = -91.5696823625976

x27 = -0.463495408493621

x28 = 65.509950316892

x29 = -60.1537558266997

x30 = -68.0077374606742

x31 = 15.2444678594553

x32 = 78.0763209312512

x33 = -24.0254403104171

x34 = 5.81968989868597

x35 = -6.74668071567321

x36 = -82.1449044018282

x37 = -61.7245521534946

x38 = 29.3816348006094

x39 = 32.5232274541992

x40 = -28.7378292908018

x41 = 40.3772090881737

x42 = -22.4546439836222

x43 = 27.8108384738145

x44 = -25.596236637212

x45 = -36.5918109247762

x46 = -80.5741080750334

x47 = 34.0940237809941

x48 = -3.60508806208341

x49 = -39.733403578366

x50 = 23.0984494934298

x51 = 81.217913584841

x52 = -74.2909227678538

x53 = -2.03429173528852

x54 = 19.95685683984

x55 = -58.5829594999048

x56 = -9.888273369263

x57 = 63.9391539900971

x58 = 18.3860605130451

x59 = 43.5188017417635

x60 = -31.8794219443916

x61 = -14.6006623496477

x62 = -75.8617190946487

x63 = -20.8838476568273

x64 = 62.3683576633022

x65 = 89.0718952188155

x66 = -46.0165888855456

x67 = 70.2223392972767

x68 = 87.5010988920206

x69 = -42.8749962319558

x70 = -89.9988860358027

x71 = 92.2134878724053

x72 = 41.9480054149686

x73 = -66.4369411338793

x74 = 84.3595062384308

x75 = -96.2820713429823

x76 = 4.24889357189107

x77 = -86.8572933822129

x78 = -79.0033117482384

x79 = -55.441366846315

x80 = -50.7289778659303

x81 = -33.4502182711865

x82 = 98.4966731795849

x83 = 1.10730091830128

x84 = 12.1028752058656

x85 = 13.6736715326604

x86 = 48.2311907221482

x87 = 73.3639319508665

x88 = 57.6559686829176

x89 = -88.4280897090078

x90 = 10.5320788790707

x91 = -53.8705705195201

x92 = -64.8661448070844

x93 = -30.3086256175967

x94 = 26.2400421470196

x95 = -38.1626072515711

x96 = -94.7112750161874

x97 = 67.0807466436869

x98 = 100.06746950638

x99 = -17.7422550032375

x100 = -16.1714586764426

x101 = 7.39048622548086

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