tan(2*x+pi/4)=-1 (уравнение)

Найду корень уравнения: tan(2*x+pi/4)=-1

Вы ввели

   /      pi\     
tan|2*x + --| = -1
   \      4 /     

$$\tan{\left(2 x + \frac{\pi}{4} \right)} = -1$$

Подробное решение

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

Быстрый ответ

     -pi 
x1 = ----
      4  

$$x_{1} = - \frac{\pi}{4}$$

Сумма и произведение корней

сумма

    pi
0 - --
    4 

$$- \frac{\pi}{4} + 0$$

=

-pi 
----
 4  

$$- \frac{\pi}{4}$$

произведение

  -pi 
1*----
   4  

$$1 \left(- \frac{\pi}{4}\right)$$

=

-pi 
----
 4  

$$- \frac{\pi}{4}$$

Численный ответ

x1 = 24.3473430653209

x2 = 38.484510006475

x3 = -80.8960108299372

x4 = -93.4623814442964

x5 = 68.329640215578

x6 = -10.2101761241668

x7 = -11.7809724509617

x8 = -54.1924732744239

x9 = -44.7676953136546

x10 = 91.8915851175014

x11 = -3.92699081698724

x12 = 71.4712328691678

x13 = -63.6172512351933

x14 = 29.0597320457056

x15 = -18.0641577581413

x16 = 73.0420291959627

x17 = 16.4933614313464

x18 = 87.1791961371168

x19 = -74.6128255227576

x20 = -88.7499924639117

x21 = -5.49778714378214

x22 = -69.9004365423729

x23 = 63.6172512351933

x24 = -33.7721210260903

x25 = -71.4712328691678

x26 = -36.9137136796801

x27 = 35.3429173528852

x28 = 43.1968989868597

x29 = -47.9092879672443

x30 = -8.63937979737193

x31 = 51.0508806208341

x32 = -49.4800842940392

x33 = 7.06858347057703

x34 = 3.92699081698724

x35 = -2.35619449019234

x36 = -82.4668071567321

x37 = 55.7632696012188

x38 = 11.7809724509617

x39 = -46.3384916404494

x40 = 19.6349540849362

x41 = -68.329640215578

x42 = 18.0641577581413

x43 = -0.785398163397448

x44 = -77.7544181763474

x45 = 32.2013246992954

x46 = 40.0553063332699

x47 = 10.2101761241668

x48 = -25.9181393921158

x49 = -66.7588438887831

x50 = -91.8915851175014

x51 = 65.1880475619882

x52 = -41.6261026600648

x53 = -55.7632696012188

x54 = 60.4756585816035

x55 = -58.9048622548086

x56 = -32.2013246992954

x57 = 49.4800842940392

x58 = 2.35619449019234

x59 = -16.4933614313464

x60 = -85.6083998103219

x61 = -38.484510006475

x62 = 90.3207887907066

x63 = 21.2057504117311

x64 = -24.3473430653209

x65 = 79.3252145031423

x66 = 46.3384916404494

x67 = -27.4889357189107

x68 = 82.4668071567321

x69 = -14.9225651045515

x70 = -40.0553063332699

x71 = -60.4756585816035

x72 = 5.49778714378214

x73 = 84.037603483527

x74 = 93.4623814442964

x75 = 99.7455667514759

x76 = 62.0464549083984

x77 = 69.9004365423729

x78 = -30.6305283725005

x79 = 98.174770424681

x80 = -76.1836218495525

x81 = 57.3340659280137

x82 = -84.037603483527

x83 = -96.6039740978861

x84 = 85.6083998103219

x85 = 77.7544181763474

x86 = 27.4889357189107

x87 = 54.1924732744239

x88 = 25.9181393921158

x89 = 76.1836218495525

x90 = 13.3517687777566

x91 = -98.174770424681

x92 = 33.7721210260903

x93 = -90.3207887907066

x94 = -99.7455667514759

x95 = -52.621676947629

x96 = -19.6349540849362

x97 = 41.6261026600648

x98 = 95.0331777710912

x99 = -22.776546738526

x100 = -62.0464549083984

x101 = 47.9092879672443

График