cosx=2/3 (уравнение)

Найду корень уравнения: cosx=2/3

Вы ввели

cos(x) = 2/3

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

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{2}{3}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{2}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{2}{3} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{2}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{2}{3} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(2/3) + 2*pi

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

x2 = acos(2/3)

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

Сумма и произведение корней

сумма

0 + -acos(2/3) + 2*pi + acos(2/3)

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

=

2*pi

$$2 \pi$$

произведение

1*(-acos(2/3) + 2*pi)*acos(2/3)

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

=

(-acos(2/3) + 2*pi)*acos(2/3)

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

Численный ответ

x1 = -44.823365820825

x2 = 36.8580431725096

x3 = -19.6906245921067

x4 = 13.4074392849271

x5 = -36.8580431725096

x6 = 69.9561070495434

x7 = 76.239292356723

x8 = -69.9561070495434

x9 = 49.4244137868688

x10 = -57.3897364351842

x11 = -80.8403403227667

x12 = 74.5571550155871

x13 = 19.6906245921067

x14 = -55.7075990940483

x15 = -24.2916725581504

x16 = 11.7253019437912

x17 = -76.239292356723

x18 = 63.6729217423638

x19 = -101.372033585441

x20 = -13.4074392849271

x21 = -63.6729217423638

x22 = -88.8056629710821

x23 = 88.8056629710821

x24 = -87.1235256299463

x25 = 30.57485786533

x26 = 87.1235256299463

x27 = 61.9907844012279

x28 = 57.3897364351842

x29 = -18.0084872509708

x30 = -68.2739697084075

x31 = -74.5571550155871

x32 = -43.1412284796892

x33 = 24.2916725581504

x34 = 25.9738098992863

x35 = -0.84106867056793

x36 = 7.12425397774752

x37 = 82.5224776639025

x38 = -7.12425397774752

x39 = -93.4067109371259

x40 = -61.9907844012279

x41 = 51.1065511280046

x42 = 68.2739697084075

x43 = 80.8403403227667

x44 = -38.5401805136454

x45 = 93.4067109371259

x46 = 95.0888482782617

x47 = -25.9738098992863

x48 = 55.7075990940483

x49 = 32.2569952064659

x50 = -51.1065511280046

x51 = -99.6898962443055

x52 = 0.84106867056793

x53 = 5.44211663661166

x54 = -11.7253019437912

x55 = 99.6898962443055

x56 = -30.57485786533

x57 = -5.44211663661166

x58 = 38.5401805136454

x59 = -49.4244137868688

x60 = 43.1412284796892

x61 = -32.2569952064659

x62 = 44.823365820825

x63 = -95.0888482782617

x64 = 18.0084872509708

x65 = -82.5224776639025

График