cos(x)=1/6 (уравнение)

Найду корень уравнения: cos(x)=1/6

Вы ввели

cos(x) = 1/6

$$\cos{\left(x \right)} = \frac{1}{6}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{1}{6}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{6} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{6} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{6} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{6} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(1/6) + 2*pi

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

x2 = acos(1/6)

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

Сумма и произведение корней

сумма

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

$$\operatorname{acos}{\left(\frac{1}{6} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{1}{6} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

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

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

=

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

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

Численный ответ

x1 = -67.7116901314002

x2 = -17.4462076739636

x3 = -76.8015719337302

x4 = 23.7293929811431

x5 = 83.0847572409098

x6 = -13.9697188619344

x7 = -92.8444313601186

x8 = -57.9520160121915

x9 = 26.5360894762936

x10 = 20.252904169114

x11 = -89.3679425480894

x12 = -20.252904169114

x13 = 36.2957635955023

x14 = -64.2352013193711

x15 = 32.8192747834731

x16 = 13.9697188619344

x17 = 48.8621342098615

x18 = -70.5183866265507

x19 = 55.1453195170411

x20 = 64.2352013193711

x21 = -95.651127855269

x22 = -7.68653355475479

x23 = 30.0125782883227

x24 = 57.9520160121915

x25 = 86.561246052939

x26 = -83.0847572409098

x27 = -73.9948754385798

x28 = 11.163022366784

x29 = 39.1024600906527

x30 = 17.4462076739636

x31 = -42.5789489026819

x32 = 7.68653355475479

x33 = -55.1453195170411

x34 = 89.3679425480894

x35 = -48.8621342098615

x36 = 67.7116901314002

x37 = 95.651127855269

x38 = 80.2780607457594

x39 = -61.4285048242207

x40 = -4.87983705960438

x41 = -80.2780607457594

x42 = -86.561246052939

x43 = 61.4285048242207

x44 = -23.7293929811431

x45 = -30.0125782883227

x46 = 73.9948754385798

x47 = 45.3856453978323

x48 = -39.1024600906527

x49 = -45.3856453978323

x50 = -32.8192747834731

x51 = 99.1276166672982

x52 = 92.8444313601186

x53 = 4.87983705960438

x54 = -36.2957635955023

x55 = -11.163022366784

x56 = -51.6688307050119

x57 = 42.5789489026819

x58 = -1.40334824757521

x59 = -99.1276166672982

x60 = 51.6688307050119

x61 = 1.40334824757521

x62 = -26.5360894762936

x63 = 70.5183866265507

x64 = 76.8015719337302

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