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
$$5 x = \pi n$$
$$5 x = \pi n - \pi$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$5$$
получим ответ:
$$x_{1} = \frac{\pi n}{5}$$
$$x_{2} = \frac{\pi n}{5} - \frac{\pi}{5}$$

Сумма и произведение корней

сумма

        2*pi
0 + 0 + ----
         5  

$$\left(0 + 0\right) + \frac{2 \pi}{5}$$

=

2*pi
----
 5  

$$\frac{2 \pi}{5}$$

произведение

    2*pi
1*0*----
     5  

$$1 \cdot 0 \cdot \frac{2 \pi}{5}$$

=

0

$$0$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     2*pi
x2 = ----
      5  

$$x_{2} = \frac{2 \pi}{5}$$

Численный ответ

x1 = 16.3362817467814

x2 = -60.318578900558

x3 = 46.4955711838258

x4 = -51.5221196092399

x5 = -3.76991116860665

x6 = -54.0353933922214

x7 = 87.964594334643

x8 = -33.9292008684763

x9 = 84.194683166022

x10 = -40.2123858698858

x11 = 80.4247718480035

x12 = 87.964594521503

x13 = -30.1592893837491

x14 = -10.0530964446729

x15 = 3.76991127936187

x16 = 57.8053049216293

x17 = -7.53982245823079

x18 = 77.9114978757725

x19 = 27.6460153227835

x20 = -70.3716755472607

x21 = -17.5929189394225

x22 = 6.28318528457691

x23 = 54.0353935823421

x24 = 98.0176907673994

x25 = 81.6814090416849

x26 = -25955.8385039809

x27 = -21.3628298365805

x28 = -84.1946830206302

x29 = -61.5752160942579

x30 = 30.1592895730315

x31 = -16.3362817797903

x32 = 50.2654824464091

x33 = 94.2477796093535

x34 = 224.938034015581

x35 = -54.0353936076251

x36 = -41.4690231067985

x37 = 47.7522084268426

x38 = -26.3893785105158

x39 = 36.44247469426

x40 = -50.2654823701436

x41 = 22.6194672010184

x42 = 37.6991119102069

x43 = 13.8230077695553

x44 = -37.6991118762964

x45 = -11.3097333173398

x46 = 33.9292007163403

x47 = 6.28318533541917

x48 = 40.2123859974777

x49 = -43.9822971748788

x50 = -92.991142729168

x51 = -85.451320246161

x52 = 0.0

x53 = -94.2477795154135

x54 = -64.0884900664919

x55 = -47.7522083329142

x56 = 12.566370563265

x57 = -91.7345054958578

x58 = -20.1061929084272

x59 = -95.5044167584314

x60 = 100.530964835454

x61 = -27.6460154115949

x62 = -31.4159265592484

x63 = -71.6283125691559

x64 = 2.51327403695665

x65 = 23.8761042483927

x66 = 43.9822971691424

x67 = -98.0176907731277

x68 = 56.5486676960883

x69 = 66.601764277558

x70 = 74.1415867470461

x71 = 70.3716753731075

x72 = 91.7345055721108

x73 = 71.6283123949312

x74 = -74.1415865382296

x75 = 60.3185789059642

x76 = -67.8584011952071

x77 = -81.6814090363008

x78 = -6.28318522783685

x79 = -13.8230076041287

x80 = 90.4778683330187

x81 = -87.9645943599455

x82 = 10.0530963763218

x83 = -75.3982236646619

x84 = 67.8584014040323

x85 = 26.3893782163924

x86 = 49.0088452290908

x87 = -57.8053047762502

График