sin5x+cos5x=0 (уравнение)

Найду корень уравнения: sin5x+cos5x=0

Вы ввели

sin(5*x) + cos(5*x) = 0

$$\sin{\left(5 x \right)} + \cos{\left(5 x \right)} = 0$$

Подробное решение

Дано уравнение
$$\sin{\left(5 x \right)} + \cos{\left(5 x \right)} = 0$$
преобразуем:
$$\frac{\sin{\left(5 x \right)}}{\cos{\left(5 x \right)}} = -1$$
или
$$\tan{\left(5 x \right)} = -1$$
- 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

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

=

-pi 
----
 20 

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

произведение

  -pi 
1*----
   20 

$$1 \left(- \frac{\pi}{20}\right)$$

=

-pi 
----
 20 

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

Численный ответ

x1 = 8.01106126665397

x2 = -79.9535330338602

x3 = 68.329640215578

x4 = -41.6261026600648

x5 = -27.8030949842697

x6 = -29.0597320457056

x7 = 58.2765437240907

x8 = 78.3827367070653

x9 = -56.0774288665778

x10 = -22.776546738526

x11 = -37.856191475757

x12 = -61.7322956430394

x13 = -57.9623844587317

x14 = -39.7411470679109

x15 = 4.24115008234622

x16 = -51.6791991515521

x17 = 24.3473430653209

x18 = 82.1526478913731

x19 = -81.8384886260141

x20 = -34.0862802914493

x21 = 100.373885282194

x22 = 46.3384916404494

x23 = 97.8606111593221

x24 = -59.8473400508856

x25 = -69.9004365423729

x26 = 48.2234472326033

x27 = 84.037603483527

x28 = -15.8650429006285

x29 = 70.2145958077319

x30 = -68.015480950219

x31 = -6.44026493985908

x32 = 90.3207887907066

x33 = 16.1792021659874

x34 = -83.723444218168

x35 = -63.6172512351933

x36 = 50.1084028247572

x37 = -46.0243323750905

x38 = 94.0906999750143

x39 = -7.69690200129499

x40 = 51.9933584169111

x41 = -47.9092879672443

x42 = -91.8915851175014

x43 = 26.2322986574748

x44 = -66.1305253580651

x45 = -71.7853921345268

x46 = 53.878314009065

x47 = 2.35619449019234

x48 = 19.9491133502952

x49 = 31.8871654339364

x50 = -90.0066295253476

x51 = 6.1261056745001

x52 = -24.0331837999619

x53 = -49.7942435593982

x54 = -3.92699081698724

x55 = 92.2057443828604

x56 = -19.6349540849362

x57 = -12.0951317163207

x58 = -73.6703477266806

x59 = -78.0685774417064

x60 = -2.04203522483337

x61 = 57.0199066626547

x62 = 95.9756555671682

x63 = 85.9225590756809

x64 = -44.1393767829366

x65 = -88.1216739331937

x66 = 28.1172542496287

x67 = -5.81194640914112

x68 = 14.2942465738336

x69 = -105.714592793297

x70 = 41.9402619254237

x71 = -93.7765407096553

x72 = 62.0464549083984

x73 = 75.8694625841935

x74 = 21.2057504117311

x75 = 60.1614993162445

x76 = -35.9712358836031

x77 = 9.89601685880785

x78 = -25.9181393921158

x79 = 18.0641577581413

x80 = 30.0022098417825

x81 = -100.059726016835

x82 = -29.6880505764235

x83 = 80.2676922992192

x84 = 35.0287580875262

x85 = 63.9314105005523

x86 = 36.2853951489621

x87 = 123.621670918758

x88 = -13.9800873084746

x89 = -17.7499984927823

x90 = 72.0995513998858

x91 = 40.0553063332699

x92 = 38.170350741116

x93 = -95.6614963018092

x94 = 73.9845069920396

График