cos(2x)=1/2 (уравнение)

Найду корень уравнения: cos(2x)=1/2

Вы ввели

cos(2*x) = 1/2

$$\cos{\left(2 x \right)} = \frac{1}{2}$$

Подробное решение

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

Быстрый ответ

     pi
x1 = --
     6 

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

     5*pi
x2 = ----
      6  

$$x_{2} = \frac{5 \pi}{6}$$

Численный ответ

x1 = -19.3731546971371

x2 = 3.66519142918809

x3 = 78.0162175641465

x4 = 93.7241808320955

x5 = -43.4586983746588

x6 = -3.66519142918809

x7 = -87.4409955249159

x8 = -82.2050077689329

x9 = 131.423292675173

x10 = -69.6386371545737

x11 = -31.9395253114962

x12 = 68.5914396033772

x13 = -71.733032256967

x14 = 30.8923277602996

x15 = 0.523598775598299

x16 = -9.94837673636768

x17 = 56.025068989018

x18 = 66.497044500984

x19 = 91.6297857297023

x20 = -41.3643032722656

x21 = -12.0427718387609

x22 = 27.7507351067098

x23 = -217.293491873294

x24 = -81.1578102177363

x25 = -16.2315620435473

x26 = -5.75958653158129

x27 = -90.5825881785057

x28 = 52.8834763354282

x29 = -91.6297857297023

x30 = 16.2315620435473

x31 = -40.317105721069

x32 = -34.0339204138894

x33 = -21.4675497995303

x34 = 38.2227106186758

x35 = -84.2994028713261

x36 = 22.5147473507269

x37 = 41.3643032722656

x38 = 62.3082542961976

x39 = 82.2050077689329

x40 = 85.3466004225227

x41 = -49.7418836818384

x42 = -46.6002910282486

x43 = -85.3466004225227

x44 = -56.025068989018

x45 = 19.3731546971371

x46 = -97.9129710368819

x47 = -65.4498469497874

x48 = 44.5058959258554

x49 = 53.9306738866248

x50 = 84.2994028713261

x51 = -7272.26339428477

x52 = -53.9306738866248

x53 = 125.140107367993

x54 = 97.9129710368819

x55 = 75.9218224617533

x56 = 49.7418836818384

x57 = 63.3554518473942

x58 = -18.3259571459405

x59 = 5.75958653158129

x60 = -100.007366139275

x61 = -47.6474885794452

x62 = -25.6563400043166

x63 = 88.4881930761125

x64 = -27.7507351067098

x65 = 2.61799387799149

x66 = 100.007366139275

x67 = 12.0427718387609

x68 = 31.9395253114962

x69 = 24.60914245312

x70 = -68.5914396033772

x71 = 25.6563400043166

x72 = 96.8657734856853

x73 = -2685.53812004368

x74 = -62.3082542961976

x75 = -60.2138591938044

x76 = -2.61799387799149

x77 = 74.8746249105567

x78 = 90.5825881785057

x79 = 69.6386371545737

x80 = -93.7241808320955

x81 = 46.6002910282486

x82 = -24.60914245312

x83 = 40.317105721069

x84 = 60.2138591938044

x85 = -75.9218224617533

x86 = 8.90117918517108

x87 = -63.3554518473942

x88 = 18.3259571459405

x89 = -13.0899693899575

x90 = -78.0162175641465

x91 = 9.94837673636768

x92 = -1152.44090509186

x93 = 47.6474885794452

x94 = 71.733032256967

x95 = -35.081117965086

x96 = 34.0339204138894

x97 = -38.2227106186758

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