cos(x)=-5\6 (уравнение)

Найду корень уравнения: cos(x)=-5\6

Вы ввели

cos(x) = -5/6

$$\cos{\left(x \right)} = - \frac{5}{6}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = - \frac{5}{6}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(- \frac{5}{6} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{5}{6} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(- \frac{5}{6} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{5}{6} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(-5/6) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(- \frac{5}{6} \right)} + 2 \pi$$

x2 = acos(-5/6)

$$x_{2} = \operatorname{acos}{\left(- \frac{5}{6} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(-5/6) + 2*pi + acos(-5/6)

$$\operatorname{acos}{\left(- \frac{5}{6} \right)} + \left(0 + \left(- \operatorname{acos}{\left(- \frac{5}{6} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(-5/6) + 2*pi)*acos(-5/6)

$$1 \left(- \operatorname{acos}{\left(- \frac{5}{6} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{5}{6} \right)}$$

=

(-acos(-5/6) + 2*pi)*acos(-5/6)

$$\left(- \operatorname{acos}{\left(- \frac{5}{6} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{5}{6} \right)}$$

Численный ответ

x1 = 47.709575347304

x2 = -84.2373161034673

x3 = -35.1432047329449

x4 = 72.8423165760224

x5 = 41.4263900401245

x6 = -59.1045748747489

x7 = 3.72727819704694

x8 = -9301.67016173592

x9 = 66.5591312688428

x10 = -15.1222777244918

x11 = -40.2550189532102

x12 = -60.2759459616632

x13 = -8.83909241731223

x14 = -96.8036867178264

x15 = -1486.55901069143

x16 = -3.72727819704694

x17 = 35.1432047329449

x18 = -77.9541307962877

x19 = 28.8600194257653

x20 = 52.8213895675693

x21 = 27.688648338851

x22 = 2.55590711013264

x23 = -41.4263900401245

x24 = 96.8036867178264

x25 = 59.1045748747489

x26 = 1064.41422402348

x27 = 71.6709454891081

x28 = -52.8213895675693

x29 = -16.2936488114061

x30 = 97.9750578047407

x31 = 21.4054630316714

x32 = 22.5768341185857

x33 = 77.9541307962877

x34 = 65.3877601819285

x35 = -79.125501883202

x36 = -72.8423165760224

x37 = -27.688648338851

x38 = 33.9718336460306

x39 = -91.6918724975611

x40 = -53.9927606544836

x41 = -47.709575347304

x42 = 40.2550189532102

x43 = 10.0104635042265

x44 = 46.5382042603897

x45 = -90.5205014106469

x46 = -33.9718336460306

x47 = -85.4086871903816

x48 = -22.5768341185857

x49 = 15.1222777244918

x50 = -97.9750578047407

x51 = 53.9927606544836

x52 = -10.0104635042265

x53 = -71.6709454891081

x54 = 60.2759459616632

x55 = 16.2936488114061

x56 = -3797.5998326466

x57 = 79.125501883202

x58 = -21.4054630316714

x59 = -65.3877601819285

x60 = -28.8600194257653

x61 = 8.83909241731223

x62 = 84.2373161034673

x63 = 85.4086871903816

x64 = 380.718396627822

x65 = -66.5591312688428

x66 = 91.6918724975611

x67 = -2.55590711013264

x68 = 90.5205014106469

x69 = -46.5382042603897

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