tan(5*x)=1 (уравнение)

Найду корень уравнения: tan(5*x)=1

Вы ввели

tan(5*x) = 1

$$\tan{\left(5 x \right)} = 1$$

Подробное решение

Дано уравнение
$$\tan{\left(5 x \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$5 x = \pi n + \operatorname{atan}{\left(1 \right)}$$
Или
$$5 x = \pi n + \frac{\pi}{4}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$5$$
получим ответ:
$$x_{1} = \frac{\pi n}{5} + \frac{\pi}{20}$$

Быстрый ответ

     pi
x1 = --
     20

$$x_{1} = \frac{\pi}{20}$$

Сумма и произведение корней

сумма

    pi
0 + --
    20

$$0 + \frac{\pi}{20}$$

=

pi
--
20

$$\frac{\pi}{20}$$

произведение

  pi
1*--
  20

$$1 \frac{\pi}{20}$$

=

pi
--
20

$$\frac{\pi}{20}$$

Численный ответ

x1 = 62.3606141737574

x2 = -73.9845069920396

x3 = 34.0862802914493

x4 = 66.1305253580651

x5 = 16.4933614313464

x6 = 26.5464579228338

x7 = -61.4181363776805

x8 = 13.9800873084746

x9 = 57.9623844587317

x10 = -21.8340689424491

x11 = 30.3163691071415

x12 = 50.4225620901162

x13 = 96.2898148325272

x14 = -63.9314105005523

x15 = 56.0774288665778

x16 = -25.6039801267568

x17 = 100.059726016835

x18 = -8.01106126665397

x19 = -97.8606111593221

x20 = -91.5774258521425

x21 = -75.8694625841935

x22 = 10.2101761241668

x23 = -53.878314009065

x24 = -87.8075146678347

x25 = 40.3694655986288

x26 = -95.9756555671682

x27 = 32.2013246992954

x28 = -5.49778714378214

x29 = -27.4889357189107

x30 = -31.8871654339364

x31 = 78.0685774417064

x32 = 86.2367183410398

x33 = 4.5553093477052

x34 = -89.6924702599886

x35 = 68.015480950219

x36 = -55.7632696012188

x37 = 54.1924732744239

x38 = 52.3075176822701

x39 = -69.5862772770139

x40 = 6.44026493985908

x41 = 72.4137106652447

x42 = 60.4756585816035

x43 = -15.5508836352695

x44 = -37.542032210398

x45 = 98.174770424681

x46 = 64.2455697659113

x47 = 84.3517627488859

x48 = 2.04203522483337

x49 = -33.7721210260903

x50 = -65.8163660927062

x51 = -1.72787595947439

x52 = 28.4314135149876

x53 = 76.1836218495525

x54 = -99.7455667514759

x55 = -81.5243293606551

x56 = -77.7544181763474

x57 = -35.6570766182442

x58 = -93.4623814442964

x59 = -59.5331807855266

x60 = 74.2986662573986

x61 = 0.15707963267949

x62 = 70.5287550730909

x63 = -57.6482251933727

x64 = 94.4048592403733

x65 = -23.7190245346029

x66 = -85.9225590756809

x67 = -67.70132168486

x68 = 22.148228207808

x69 = 38.484510006475

x70 = 44.1393767829366

x71 = 8.32522053201295

x72 = 35.9712358836031

x73 = 92.5199036482194

x74 = -41.9402619254237

x75 = 88.1216739331937

x76 = -39.4269878025519

x77 = -19.9491133502952

x78 = -11.7809724509617

x79 = -3.61283155162826

x80 = -79.6393737685013

x81 = 24.0331837999619

x82 = -17.4358392274234

x83 = 82.4668071567321

x84 = -43.8252175175776

x85 = -51.9933584169111

x86 = 46.0243323750905

x87 = -71.4712328691678

x88 = 18.3783170235003

x89 = 12.0951317163207

x90 = -47.5951287018854

x91 = 80.5818515645782

x92 = 48.5376064979623

x93 = 42.2544211907827

x94 = -9.89601685880785

x95 = -30.0022098417825

x96 = 90.0066295253476

x97 = -13.6659280431156

x98 = -84.037603483527

x99 = -49.4800842940392

x100 = -45.7101731097315

x101 = 20.2632726156542

График