cos(x)=1/8 (уравнение)

Найду корень уравнения: cos(x)=1/8

Вы ввели

cos(x) = 1/8

$$\cos{\left(x \right)} = \frac{1}{8}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{1}{8}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{8} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{8} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{8} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{8} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(1/8) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(\frac{1}{8} \right)} + 2 \pi$$

x2 = acos(1/8)

$$x_{2} = \operatorname{acos}{\left(\frac{1}{8} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(1/8) + 2*pi + acos(1/8)

$$\operatorname{acos}{\left(\frac{1}{8} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{1}{8} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(1/8) + 2*pi)*acos(1/8)

$$1 \left(- \operatorname{acos}{\left(\frac{1}{8} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{8} \right)}$$

=

(-acos(1/8) + 2*pi)*acos(1/8)

$$\left(- \operatorname{acos}{\left(\frac{1}{8} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{8} \right)}$$

Численный ответ

x1 = -36.2536433474507

x2 = 26.5782097243452

x3 = -17.4040874259119

x4 = -1.44546849562683

x5 = 73.9527551905282

x6 = -7.72865380280642

x7 = 20.2950244171656

x8 = 17.4040874259119

x9 = 23.6872727330915

x10 = 7.72865380280642

x11 = -48.8200139618099

x12 = -39.1445803387044

x13 = -73.9527551905282

x14 = -23.6872727330915

x15 = -86.5191258048874

x16 = -92.802311112067

x17 = 45.4277656458839

x18 = -29.9704580402711

x19 = -51.7109509530635

x20 = -57.9941362602431

x21 = 99.0854964192466

x22 = 14.011839109986

x23 = -99.0854964192466

x24 = -95.6932481033206

x25 = -67.6695698833486

x26 = 89.410062796141

x27 = -11.1209021187323

x28 = 36.2536433474507

x29 = -20.2950244171656

x30 = 95.6932481033206

x31 = 42.5368286546303

x32 = -83.1268774889615

x33 = 1.44546849562683

x34 = 92.802311112067

x35 = 61.386384576169

x36 = 57.9941362602431

x37 = 83.1268774889615

x38 = 86.5191258048874

x39 = 64.2773215674227

x40 = 11.1209021187323

x41 = 48.8200139618099

x42 = 67.6695698833486

x43 = -80.2359404977078

x44 = -26.5782097243452

x45 = -76.8436921817819

x46 = -42.5368286546303

x47 = -70.5605068746023

x48 = 32.8613950315248

x49 = 4.83771681155276

x50 = 55.1031992689894

x51 = -55.1031992689894

x52 = -45.4277656458839

x53 = 76.8436921817819

x54 = -61.386384576169

x55 = -1490.56038629719

x56 = -14.011839109986

x57 = 617.197628599226

x58 = -64.2773215674227

x59 = 80.2359404977078

x60 = 29.9704580402711

x61 = -89.410062796141

x62 = 51.7109509530635

x63 = 39.1445803387044

x64 = -4.83771681155276

x65 = 70.5605068746023

x66 = -32.8613950315248

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