cosx=√3/2 (уравнение)

Найду корень уравнения: cosx=√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 = -81.1578102177363

x2 = 68.5914396033772

x3 = 30.8923277602996

x4 = 37.1755130674792

x5 = -19.3731546971371

x6 = -68.5914396033772

x7 = 56.025068989018

x8 = 69.6386371545737

x9 = -100.007366139275

x10 = 5.75958653158129

x11 = 31.9395253114962

x12 = 19.3731546971371

x13 = 63.3554518473942

x14 = -24.60914245312

x15 = -6.80678408277789

x16 = 75.9218224617533

x17 = -50.789081233035

x18 = 13.0899693899575

x19 = 194.255145746969

x20 = 81.1578102177363

x21 = 25.6563400043166

x22 = -12.0427718387609

x23 = -49.7418836818384

x24 = -25.6563400043166

x25 = 12.0427718387609

x26 = -56.025068989018

x27 = -30.8923277602996

x28 = -13.0899693899575

x29 = -57.0722665402146

x30 = -38.2227106186758

x31 = -18.3259571459405

x32 = 43.4586983746588

x33 = 38.2227106186758

x34 = -37.1755130674792

x35 = -31.9395253114962

x36 = -0.523598775598299

x37 = -74.8746249105567

x38 = 88.4881930761125

x39 = 62.3082542961976

x40 = 74.8746249105567

x41 = 18.3259571459405

x42 = 87.4409955249159

x43 = -88.4881930761125

x44 = 93.7241808320955

x45 = -63.3554518473942

x46 = -75.9218224617533

x47 = -69.6386371545737

x48 = -82.2050077689329

x49 = -62.3082542961976

x50 = -93.7241808320955

x51 = -44.5058959258554

x52 = -101.054563690472

x53 = 1168.1488683598

x54 = 94.7713783832921

x55 = -94.7713783832921

x56 = 82.2050077689329

x57 = 49.7418836818384

x58 = 50.789081233035

x59 = 100.007366139275

x60 = 44.5058959258554

x61 = 24.60914245312

x62 = -43.4586983746588

x63 = 0.523598775598299

x64 = -87.4409955249159

x65 = 6.80678408277789

x66 = 57.0722665402146

x67 = -5.75958653158129

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