cos(x)=√3/2 (уравнение)

Найду корень уравнения: cos(x)=√3/2

Вы ввели

           ___
         \/ 3 
cos(x) = -----
           2  

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

Подробное решение

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

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

Сумма и произведение корней

сумма

    pi   11*pi
0 + -- + -----
    6      6  

$$\left(0 + \frac{\pi}{6}\right) + \frac{11 \pi}{6}$$

=

2*pi

$$2 \pi$$

произведение

  pi 11*pi
1*--*-----
  6    6  

$$\frac{11 \pi}{6} \cdot 1 \frac{\pi}{6}$$

=

     2
11*pi 
------
  36  

$$\frac{11 \pi^{2}}{36}$$

Численный ответ

x1 = -62.3082542961976

x2 = 37.1755130674792

x3 = 74.8746249105567

x4 = -101.054563690472

x5 = 6.80678408277789

x6 = -49.7418836818384

x7 = -5.75958653158129

x8 = -37.1755130674792

x9 = -81.1578102177363

x10 = 94.7713783832921

x11 = -87.4409955249159

x12 = 81.1578102177363

x13 = -94.7713783832921

x14 = -50.789081233035

x15 = 24.60914245312

x16 = -74.8746249105567

x17 = 82.2050077689329

x18 = 100.007366139275

x19 = -19.3731546971371

x20 = 68.5914396033772

x21 = 13.0899693899575

x22 = 43.4586983746588

x23 = 50.789081233035

x24 = -0.523598775598299

x25 = -12.0427718387609

x26 = -93.7241808320955

x27 = -75.9218224617533

x28 = 25.6563400043166

x29 = 30.8923277602996

x30 = 0.523598775598299

x31 = 18.3259571459405

x32 = 69.6386371545737

x33 = -63.3554518473942

x34 = 44.5058959258554

x35 = 75.9218224617533

x36 = 1168.1488683598

x37 = 194.255145746969

x38 = -38.2227106186758

x39 = 88.4881930761125

x40 = 93.7241808320955

x41 = 57.0722665402146

x42 = -31.9395253114962

x43 = -25.6563400043166

x44 = -56.025068989018

x45 = -100.007366139275

x46 = -30.8923277602996

x47 = 63.3554518473942

x48 = 12.0427718387609

x49 = -69.6386371545737

x50 = 87.4409955249159

x51 = -57.0722665402146

x52 = -44.5058959258554

x53 = -13.0899693899575

x54 = -82.2050077689329

x55 = 38.2227106186758

x56 = 62.3082542961976

x57 = 49.7418836818384

x58 = 56.025068989018

x59 = -43.4586983746588

x60 = 5.75958653158129

x61 = -6.80678408277789

x62 = -88.4881930761125

x63 = -68.5914396033772

x64 = -18.3259571459405

x65 = 31.9395253114962

x66 = 19.3731546971371

x67 = -24.60914245312

График