cos(3x)/7=0 (уравнение)

Найду корень уравнения: cos(3x)/7=0

Вы ввели

cos(3*x)    
-------- = 0
   7        

$$\frac{\cos{\left(3 x \right)}}{7} = 0$$

Подробное решение

Дано уравнение
$$\frac{\cos{\left(3 x \right)}}{7} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$\frac{\cos{\left(3 x \right)}}{7} = 0$$

Разделим обе части ур-ния на 1/7

Ур-ние превратится в
$$\cos{\left(3 x \right)} = 0$$
Это ур-ние преобразуется в
$$3 x = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$3 x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Или
$$3 x = \pi n + \frac{\pi}{2}$$
$$3 x = \pi n - \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{6}$$
$$x_{2} = \frac{\pi n}{3} - \frac{\pi}{6}$$

Быстрый ответ

     pi
x1 = --
     6 

$$x_{1} = \frac{\pi}{6}$$

     pi
x2 = --
     2 

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

Сумма и произведение корней

сумма

    pi   pi
0 + -- + --
    6    2 

$$\left(0 + \frac{\pi}{6}\right) + \frac{\pi}{2}$$

=

2*pi
----
 3  

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

произведение

  pi pi
1*--*--
  6  2 

$$\frac{\pi}{2} \cdot 1 \frac{\pi}{6}$$

=

  2
pi 
---
 12

$$\frac{\pi^{2}}{12}$$

Численный ответ

x1 = 36.1283155162826

x2 = 2044.65321871136

x3 = -71.733032256967

x4 = -16.2315620435473

x5 = 0.523598775598299

x6 = 71.733032256967

x7 = -38.2227106186758

x8 = -31.9395253114962

x9 = 87.4409955249159

x10 = -14.1371669411541

x11 = 27.7507351067098

x12 = 84.2994028713261

x13 = 4.71238898038469

x14 = 26.7035375555132

x15 = 15.1843644923507

x16 = -91.6297857297023

x17 = -25.6563400043166

x18 = 42.4115008234622

x19 = -95.8185759344887

x20 = 68.5914396033772

x21 = -1.5707963267949

x22 = 58.1194640914112

x23 = -49.7418836818384

x24 = -84.2994028713261

x25 = -34.0339204138894

x26 = 14.1371669411541

x27 = -5.75958653158129

x28 = -75.9218224617533

x29 = -47.6474885794452

x30 = -12.0427718387609

x31 = -58.1194640914112

x32 = 34.0339204138894

x33 = 62.3082542961976

x34 = 31.9395253114962

x35 = -3.66519142918809

x36 = -43.4586983746588

x37 = 86.3937979737193

x38 = 38.2227106186758

x39 = -7.85398163397448

x40 = 12.0427718387609

x41 = 22.5147473507269

x42 = 16.2315620435473

x43 = 82.2050077689329

x44 = -65.4498469497874

x45 = 60.2138591938044

x46 = 95.8185759344887

x47 = 93.7241808320955

x48 = -80.1106126665397

x49 = -45.553093477052

x50 = -27.7507351067098

x51 = -97.9129710368819

x52 = 41.3643032722656

x53 = -89.5353906273091

x54 = 53.9306738866248

x55 = 51.8362787842316

x56 = -60.2138591938044

x57 = -61.261056745001

x58 = 73.8274273593601

x59 = 29.845130209103

x60 = 100.007366139275

x61 = 1.5707963267949

x62 = -98.9601685880785

x63 = 66.497044500984

x64 = -62.3082542961976

x65 = -21.4675497995303

x66 = -53.9306738866248

x67 = -29.845130209103

x68 = -78.0162175641465

x69 = -56.025068989018

x70 = -23.5619449019235

x71 = -82.2050077689329

x72 = 56.025068989018

x73 = 5.75958653158129

x74 = 78.0162175641465

x75 = 75.9218224617533

x76 = -67.5442420521806

x77 = -93.7241808320955

x78 = 40.317105721069

x79 = 97.9129710368819

x80 = -69.6386371545737

x81 = 91.6297857297023

x82 = 44.5058959258554

x83 = 64.4026493985908

x84 = -100.007366139275

x85 = 18.3259571459405

x86 = -73.8274273593601

x87 = 88.4881930761125

x88 = 49.7418836818384

x89 = -51.8362787842316

x90 = -19.3731546971371

x91 = 80.1106126665397

x92 = -9.94837673636768

x93 = 9.94837673636768

x94 = 7.85398163397448

x95 = 20.4203522483337

x96 = -36.1283155162826

График