(3cos3x)/2=0 (уравнение)

Найду корень уравнения: (3cos3x)/2=0

Вы ввели

3*cos(3*x)    
---------- = 0
    2         

$$\frac{3 \cos{\left(3 x \right)}}{2} = 0$$

Подробное решение

Дано уравнение
$$\frac{3 \cos{\left(3 x \right)}}{2} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$\frac{3 \cos{\left(3 x \right)}}{2} = 0$$

Разделим обе части ур-ния на 3/2

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
-- + --
6    2 

$$\frac{\pi}{6} + \frac{\pi}{2}$$

=

2*pi
----
 3  

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

произведение

pi pi
--*--
6  2 

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

=

  2
pi 
---
 12

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

Численный ответ

x1 = 71.733032256967

x2 = 34.0339204138894

x3 = 78.0162175641465

x4 = -62.3082542961976

x5 = -29.845130209103

x6 = 51.8362787842316

x7 = -84.2994028713261

x8 = 31.9395253114962

x9 = -95.8185759344887

x10 = -43.4586983746588

x11 = -12.0427718387609

x12 = -100.007366139275

x13 = 15.1843644923507

x14 = -67.5442420521806

x15 = 9.94837673636768

x16 = -56.025068989018

x17 = 29.845130209103

x18 = 40.317105721069

x19 = -3.66519142918809

x20 = -93.7241808320955

x21 = -25.6563400043166

x22 = 53.9306738866248

x23 = 38.2227106186758

x24 = 26.7035375555132

x25 = 95.8185759344887

x26 = -47.6474885794452

x27 = -27.7507351067098

x28 = 49.7418836818384

x29 = 27.7507351067098

x30 = -49.7418836818384

x31 = 4.71238898038469

x32 = -69.6386371545737

x33 = 42.4115008234622

x34 = -1.5707963267949

x35 = 91.6297857297023

x36 = 62.3082542961976

x37 = -73.8274273593601

x38 = 18.3259571459405

x39 = 12.0427718387609

x40 = -89.5353906273091

x41 = 86.3937979737193

x42 = 75.9218224617533

x43 = 41.3643032722656

x44 = 88.4881930761125

x45 = 20.4203522483337

x46 = 119.90411961201

x47 = -38.2227106186758

x48 = -5.75958653158129

x49 = -60.2138591938044

x50 = -75.9218224617533

x51 = 64.4026493985908

x52 = 68.5914396033772

x53 = 97.9129710368819

x54 = -14.1371669411541

x55 = -78.0162175641465

x56 = -51.8362787842316

x57 = -34.0339204138894

x58 = 82.2050077689329

x59 = 56.025068989018

x60 = 87.4409955249159

x61 = -80.1106126665397

x62 = 93.7241808320955

x63 = 7.85398163397448

x64 = 84.2994028713261

x65 = -23.5619449019235

x66 = -16.2315620435473

x67 = 5.75958653158129

x68 = 14.1371669411541

x69 = 80.1106126665397

x70 = -9.94837673636768

x71 = 100.007366139275

x72 = -65.4498469497874

x73 = -82.2050077689329

x74 = 22.5147473507269

x75 = 73.8274273593601

x76 = -91.6297857297023

x77 = -61.261056745001

x78 = 44.5058959258554

x79 = -31.9395253114962

x80 = 36.1283155162826

x81 = 66.497044500984

x82 = -21.4675497995303

x83 = -7.85398163397448

x84 = 60.2138591938044

x85 = -19.3731546971371

x86 = 1.5707963267949

x87 = -71.733032256967

x88 = -58.1194640914112

x89 = 16.2315620435473

x90 = 0.523598775598299

x91 = -97.9129710368819

x92 = 58.1194640914112

x93 = -45.553093477052

x94 = -36.1283155162826

x95 = -53.9306738866248

x96 = -98.9601685880785

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