cos(x)=√3/3 (уравнение)

Найду корень уравнения: cos(x)=√3/3

Вы ввели

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

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

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{\sqrt{3}}{3}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{3} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{3} \right)}$$
, где n - любое целое число

Быстрый ответ

           /  ___\       
           |\/ 3 |       
x1 = - acos|-----| + 2*pi
           \  3  /       

$$x_{1} = - \operatorname{acos}{\left(\frac{\sqrt{3}}{3} \right)} + 2 \pi$$

         /  ___\
         |\/ 3 |
x2 = acos|-----|
         \  3  /

$$x_{2} = \operatorname{acos}{\left(\frac{\sqrt{3}}{3} \right)}$$

Сумма и произведение корней

сумма

          /  ___\              /  ___\
          |\/ 3 |              |\/ 3 |
0 + - acos|-----| + 2*pi + acos|-----|
          \  3  /              \  3  /

$$\operatorname{acos}{\left(\frac{\sqrt{3}}{3} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{\sqrt{3}}{3} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

  /      /  ___\       \     /  ___\
  |      |\/ 3 |       |     |\/ 3 |
1*|- acos|-----| + 2*pi|*acos|-----|
  \      \  3  /       /     \  3  /

$$1 \left(- \operatorname{acos}{\left(\frac{\sqrt{3}}{3} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{\sqrt{3}}{3} \right)}$$

=

/      /  ___\       \     /  ___\
|      |\/ 3 |       |     |\/ 3 |
|- acos|-----| + 2*pi|*acos|-----|
\      \  3  /       /     \  3  /

$$\left(- \operatorname{acos}{\left(\frac{\sqrt{3}}{3} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{\sqrt{3}}{3} \right)}$$

Численный ответ

x1 = 43.0269805321326

x2 = 30.4606099177734

x3 = -88.9199109186387

x4 = -70.0703549971

x5 = -17.8942393034142

x6 = 36.743795224953

x7 = -5.32786868905508

x8 = 5.32786868905508

x9 = -26.0880578468429

x10 = 7.2385019253041

x11 = -43.0269805321326

x12 = -36.743795224953

x13 = 80.7260923752101

x14 = -0.955316618124509

x15 = -51.2207990755612

x16 = -61.8765364536714

x17 = 93.2924629895693

x18 = 19.8048725396633

x19 = 49.3101658393122

x20 = 76.3535403042795

x21 = 26.0880578468429

x22 = -68.1597217608509

x23 = -101.486281532998

x24 = 95.2030962258183

x25 = -99.5756482967489

x26 = -95.2030962258183

x27 = -38.654428461202

x28 = -63.7871696899204

x29 = -11.6110539962347

x30 = 99.5756482967489

x31 = -32.3712431540224

x32 = 32.3712431540224

x33 = -80.7260923752101

x34 = 0.955316618124509

x35 = 87.0092776823897

x36 = -24.1774246105938

x37 = -30.4606099177734

x38 = 13.5216872324837

x39 = -49.3101658393122

x40 = -19.8048725396633

x41 = 88.9199109186387

x42 = 3228.60193127218

x43 = 68.1597217608509

x44 = 74.4429070680305

x45 = 11.6110539962347

x46 = -87.0092776823897

x47 = -93.2924629895693

x48 = 24.1774246105938

x49 = -13.5216872324837

x50 = -55.5933511464918

x51 = 70.0703549971

x52 = 17.8942393034142

x53 = -82.6367256114591

x54 = 51.2207990755612

x55 = -76.3535403042795

x56 = 61.8765364536714

x57 = 82.6367256114591

x58 = -44.9376137683816

x59 = 55.5933511464918

x60 = -57.5039843827408

x61 = 38.654428461202

x62 = -74.4429070680305

x63 = 44.9376137683816

x64 = 57.5039843827408

x65 = 281.788022204957

x66 = 63.7871696899204

x67 = -7.2385019253041

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