cos(x)=-2/3 (уравнение)

Найду корень уравнения: cos(x)=-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

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)

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

Быстрый ответ

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

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

x2 = acos(-2/3)

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

Численный ответ

x1 = 33.7164505189198

x2 = -58.8491917476381

x3 = 65.1323770548177

x4 = 60.531329088774

x5 = -47.9649584744148

x6 = 16.5490319385169

x7 = -79.3808850103128

x8 = -60.531329088774

x9 = 47.9649584744148

x10 = -85.6640703174923

x11 = 91.9472556246719

x12 = -90.2651182835361

x13 = 54.2481437815944

x14 = 10.2658466313373

x15 = 85.6640703174923

x16 = -77.6987476691769

x17 = 52.5660064404586

x18 = -73.0976997031332

x19 = -3.98266132415772

x20 = -52.5660064404586

x21 = -27.4332652117402

x22 = -2.30052398302186

x23 = -98.2304409318515

x24 = -21.1500799045606

x25 = 96.5483035907157

x26 = -35.3985878600557

x27 = 3.98266132415772

x28 = 77.6987476691769

x29 = 22.8322172456965

x30 = -46.282821133279

x31 = 2.30052398302186

x32 = 79.3808850103128

x33 = 71.4155623619973

x34 = -16.5490319385169

x35 = -10.2658466313373

x36 = 83.9819329763565

x37 = -66.8145143959536

x38 = 8.58370929020145

x39 = -71.4155623619973

x40 = 90.2651182835361

x41 = 73.0976997031332

x42 = -91.9472556246719

x43 = -8.58370929020145

x44 = 58.8491917476381

x45 = -83.9819329763565

x46 = 98.2304409318515

x47 = -96.5483035907157

x48 = -41.6817731672352

x49 = 35.3985878600557

x50 = 66.8145143959536

x51 = 39.9996358260994

x52 = 605.486313472262

x53 = 41.6817731672352

x54 = -22.8322172456965

x55 = -29.1154025528761

x56 = -14.866894597381

x57 = 21.1500799045606

x58 = 29.1154025528761

x59 = -54.2481437815944

x60 = -65.1323770548177

x61 = 46.282821133279

x62 = 27.4332652117402

x63 = -33.7164505189198

x64 = -39.9996358260994

x65 = 14.866894597381

График