cos(5x)=-1 (уравнение)

Найду корень уравнения: cos(5x)=-1

Вы ввели

cos(5*x) = -1

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

Подробное решение

Дано уравнение
$$\cos{\left(5 x \right)} = -1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$5 x = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$5 x = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Или
$$5 x = \pi n + \pi$$
$$5 x = \pi n$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$5$$
получим ответ:
$$x_{1} = \frac{\pi n}{5} + \frac{\pi}{5}$$
$$x_{2} = \frac{\pi n}{5}$$

Быстрый ответ

     pi
x1 = --
     5 

$$x_{1} = \frac{\pi}{5}$$

Сумма и произведение корней

сумма

    pi
0 + --
    5 

$$0 + \frac{\pi}{5}$$

=

pi
--
5 

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

произведение

  pi
1*--
  5 

$$1 \frac{\pi}{5}$$

=

pi
--
5 

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

Численный ответ

x1 = -28.2743337985554

x2 = -88.5929128293176

x3 = -76.0265421900045

x4 = -69.7433569145379

x5 = 1.88495567013317

x6 = 88.5929128275364

x7 = -62.2035344450832

x8 = -96.1327351159045

x9 = 4.39822963836815

x10 = 53.4070751178469

x11 = -49.6371639904788

x12 = 14.4513261178457

x13 = -73.5132681840895

x14 = 11.9380521360494

x15 = -43.3539783700817

x16 = -15.7079632959728

x17 = 28.2743338653654

x18 = 38.3274303262717

x19 = -82.3097274652769

x20 = 58.4336232709865

x21 = 92.3628239517849

x22 = -89.8495497792564

x23 = -72.2566309424644

x24 = 49.6371638635698

x25 = 20.7345114068833

x26 = 32.0442449831012

x27 = -4.39822996477874

x28 = 68.4867197581684

x29 = 21.9911485851243

x30 = -35.8141561907284

x31 = 55.9203492962382

x32 = 8.16814098375725

x33 = 24.5044226100598

x34 = -38.3274303384674

x35 = -48.3805270261683

x36 = -39.5840675169689

x37 = 25.7610598533457

x38 = 72.2566310277294

x39 = 0.628318678042855

x40 = -19.4778745353753

x41 = 82.3097274858618

x42 = -83.5663646712746

x43 = 34.5575191286736

x44 = -59.6902604564035

x45 = 62.2035345813848

x46 = -92.362824078636

x47 = -52.1504379608442

x48 = -11.9380522418002

x49 = -21.9911485865257

x50 = 93.6194609160105

x51 = 98.6460095721798

x52 = 79.7964534971758

x53 = 76.0265421765888

x54 = 69.7433569997909

x55 = -29.5309710339385

x56 = 78.5398162651148

x57 = -25.761059750952

x58 = -97.3893722074864

x59 = 89.8495499814173

x60 = -79.7964533608863

x61 = -53.4070751146921

x62 = 45.8672528263579

x63 = -5.65486683250758

x64 = -93.6194611476217

x65 = -9.4247779996114

x66 = 44.6106157347225

x67 = -18.2212372950611

x68 = 52.1504381630217

x69 = -65.9734457656932

x70 = 5.65486677442111

x71 = 99.9026464549661

x72 = 65.9734457522645

x73 = -86.0796386460267

x74 = -32.0442450258762

x75 = 59.6902604769691

x76 = 15.7079633418309

x77 = -42.0973414872979

x78 = -106.185831553344

x79 = -49.6371639293365

x80 = -8.16814080694744

x81 = 35.8141563457511

x82 = 48.3805267946414

x83 = 86.0796387689886

x84 = -63.4601716771365

x85 = 18.2212374141788

График