2 cos x=√3 (уравнение)

Найду корень уравнения: 2 cos x=√3

Вы ввели

             ___
2*cos(x) = \/ 3 

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

Подробное решение

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

Разделим обе части ур-ния на 2

Ур-ние превратится в
$$\cos{\left(x \right)} = \frac{\sqrt{3}}{2}$$
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
Или
$$x = \pi n + \frac{\pi}{6}$$
$$x = \pi n - \frac{5 \pi}{6}$$
, где n - любое целое число

Быстрый ответ

     pi
x1 = --
     6 

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

     11*pi
x2 = -----
       6  

$$x_{2} = \frac{11 \pi}{6}$$

Численный ответ

x1 = -50.789081233035

x2 = -30.8923277602996

x3 = -87.4409955249159

x4 = -94.7713783832921

x5 = 57.0722665402146

x6 = 82.2050077689329

x7 = -63.3554518473942

x8 = -44.5058959258554

x9 = 25.6563400043166

x10 = -24.60914245312

x11 = -13.0899693899575

x12 = 31.9395253114962

x13 = 88.4881930761125

x14 = 12.0427718387609

x15 = 24.60914245312

x16 = 1168.1488683598

x17 = -62.3082542961976

x18 = 74.8746249105567

x19 = 38.2227106186758

x20 = 6.80678408277789

x21 = 94.7713783832921

x22 = 19.3731546971371

x23 = 43.4586983746588

x24 = 68.5914396033772

x25 = -93.7241808320955

x26 = 49.7418836818384

x27 = -5.75958653158129

x28 = -74.8746249105567

x29 = 0.523598775598299

x30 = -49.7418836818384

x31 = -81.1578102177363

x32 = 37.1755130674792

x33 = -31.9395253114962

x34 = 44.5058959258554

x35 = 100.007366139275

x36 = 30.8923277602996

x37 = -43.4586983746588

x38 = -101.054563690472

x39 = 18.3259571459405

x40 = -38.2227106186758

x41 = 62.3082542961976

x42 = 81.1578102177363

x43 = -69.6386371545737

x44 = 56.025068989018

x45 = 5.75958653158129

x46 = -57.0722665402146

x47 = 194.255145746969

x48 = 69.6386371545737

x49 = -37.1755130674792

x50 = 93.7241808320955

x51 = -56.025068989018

x52 = 75.9218224617533

x53 = -18.3259571459405

x54 = 87.4409955249159

x55 = 50.789081233035

x56 = -6.80678408277789

x57 = -88.4881930761125

x58 = 63.3554518473942

x59 = -75.9218224617533

x60 = -82.2050077689329

x61 = -25.6563400043166

x62 = -100.007366139275

x63 = 13.0899693899575

x64 = -12.0427718387609

x65 = -0.523598775598299

x66 = -19.3731546971371

x67 = -68.5914396033772

График