cos(x)+5/6=1 (уравнение)

Найду корень уравнения: cos(x)+5/6=1

Вы ввели

cos(x) + 5/6 = 1

$$\cos{\left(x \right)} + \frac{5}{6} = 1$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} + \frac{5}{6} = 1$$
- 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

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

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

=

2*pi

$$2 \pi$$

произведение

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

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

=

(-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 = 42.5789489026819

x2 = -39.1024600906527

x3 = 67.7116901314002

x4 = 7.68653355475479

x5 = 86.561246052939

x6 = -99.1276166672982

x7 = -95.651127855269

x8 = 4.87983705960438

x9 = 48.8621342098615

x10 = 95.651127855269

x11 = -7.68653355475479

x12 = 32.8192747834731

x13 = 57.9520160121915

x14 = -48.8621342098615

x15 = 61.4285048242207

x16 = 23.7293929811431

x17 = -20.252904169114

x18 = -92.8444313601186

x19 = 26.5360894762936

x20 = -64.2352013193711

x21 = -26.5360894762936

x22 = 13.9697188619344

x23 = 30.0125782883227

x24 = 99.1276166672982

x25 = -86.561246052939

x26 = -70.5183866265507

x27 = -80.2780607457594

x28 = 92.8444313601186

x29 = 64.2352013193711

x30 = -67.7116901314002

x31 = -45.3856453978323

x32 = 51.6688307050119

x33 = -13.9697188619344

x34 = 55.1453195170411

x35 = 73.9948754385798

x36 = -30.0125782883227

x37 = 11.163022366784

x38 = -51.6688307050119

x39 = 80.2780607457594

x40 = 89.3679425480894

x41 = -83.0847572409098

x42 = 20.252904169114

x43 = -76.8015719337302

x44 = -73.9948754385798

x45 = -4.87983705960438

x46 = 70.5183866265507

x47 = 83.0847572409098

x48 = -57.9520160121915

x49 = -23.7293929811431

x50 = -17.4462076739636

x51 = -36.2957635955023

x52 = -55.1453195170411

x53 = -89.3679425480894

x54 = 76.8015719337302

x55 = -42.5789489026819

x56 = -1.40334824757521

x57 = 39.1024600906527

x58 = 45.3856453978323

x59 = 36.2957635955023

x60 = 1.40334824757521

x61 = -32.8192747834731

x62 = -11.163022366784

x63 = -61.4285048242207

x64 = 17.4462076739636

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