cos(10*x)=0 (уравнение)

Найду корень уравнения: cos(10*x)=0

Вы ввели

cos(10*x) = 0

$$\cos{\left(10 x \right)} = 0$$

Подробное решение

Дано уравнение
$$\cos{\left(10 x \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$\cos{\left(10 x \right)} = 0$$
Это ур-ние преобразуется в
$$10 x = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$10 x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Или
$$10 x = \pi n + \frac{\pi}{2}$$
$$10 x = \pi n - \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$10$$
получим ответ:
$$x_{1} = \frac{\pi n}{10} + \frac{\pi}{20}$$
$$x_{2} = \frac{\pi n}{10} - \frac{\pi}{20}$$

Быстрый ответ

     pi
x1 = --
     20

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

     3*pi
x2 = ----
      20 

$$x_{2} = \frac{3 \pi}{20}$$

Сумма и произведение корней

сумма

    pi   3*pi
0 + -- + ----
    20    20 

$$\left(0 + \frac{\pi}{20}\right) + \frac{3 \pi}{20}$$

=

pi
--
5 

$$\frac{\pi}{5}$$

произведение

  pi 3*pi
1*--*----
  20  20 

$$\frac{3 \pi}{20} \cdot 1 \frac{\pi}{20}$$

=

    2
3*pi 
-----
 400 

$$\frac{3 \pi^{2}}{400}$$

Численный ответ

x1 = -85.9225590756809

x2 = -81.8384886260141

x3 = 28.1172542496287

x4 = 6.1261056745001

x5 = 34.0862802914493

x6 = 88.1216739331937

x7 = -31.8871654339364

x8 = -53.878314009065

x9 = -41.9402619254237

x10 = -71.7853921345268

x11 = -51.9933584169111

x12 = 92.2057443828604

x13 = -99.7455667514759

x14 = 62.6747734391164

x15 = -5.81194640914112

x16 = 30.0022098417825

x17 = 73.9845069920396

x18 = 50.1084028247572

x19 = -95.9756555671682

x20 = -19.9491133502952

x21 = -61.7322956430394

x22 = 90.0066295253476

x23 = 38.170350741116

x24 = 76.1836218495525

x25 = -79.9535330338602

x26 = -3.92699081698724

x27 = 2.04203522483337

x28 = 68.015480950219

x29 = -47.9092879672443

x30 = -22.776546738526

x31 = -8.01106126665397

x32 = 66.1305253580651

x33 = -17.7499984927823

x34 = -33.7721210260903

x35 = 51.9933584169111

x36 = 4.24115008234622

x37 = 62.0464549083984

x38 = -21.8340689424491

x39 = 37.2278729450391

x40 = -77.7544181763474

x41 = 64.2455697659113

x42 = -27.8030949842697

x43 = -90.0066295253476

x44 = 84.037603483527

x45 = 32.2013246992954

x46 = 20.2632726156542

x47 = -9.89601685880785

x48 = 0.15707963267949

x49 = -68.015480950219

x50 = -69.9004365423729

x51 = 86.2367183410398

x52 = -30.0022098417825

x53 = -13.9800873084746

x54 = 16.1792021659874

x55 = 40.0553063332699

x56 = -75.8694625841935

x57 = 70.2145958077319

x58 = -55.7632696012188

x59 = -65.8163660927062

x60 = 44.1393767829366

x61 = -91.8915851175014

x62 = -1.09955742875643

x63 = 24.0331837999619

x64 = -45.0818545790135

x65 = 8.01106126665397

x66 = -43.8252175175776

x67 = -59.8473400508856

x68 = 60.1614993162445

x69 = -39.7411470679109

x70 = 10.2101761241668

x71 = 26.2322986574748

x72 = -25.9181393921158

x73 = -49.7942435593982

x74 = 12.0951317163207

x75 = 94.0906999750143

x76 = 100.059726016835

x77 = 78.0685774417064

x78 = 54.1924732744239

x79 = -97.8606111593221

x80 = -89.6924702599886

x81 = -57.9623844587317

x82 = -87.8075146678347

x83 = 72.0995513998858

x84 = 18.0641577581413

x85 = -11.7809724509617

x86 = 42.2544211907827

x87 = 22.148228207808

x88 = -63.9314105005523

x89 = 13.9800873084746

x90 = 82.1526478913731

x91 = 98.174770424681

x92 = -35.9712358836031

x93 = 56.0774288665778

x94 = 48.2234472326033

x95 = 80.2676922992192

x96 = 46.0243323750905

x97 = -73.9845069920396

x98 = -37.856191475757

x99 = -15.8650429006285

x100 = -93.7765407096553

График