cos(x)=8/17 (уравнение)

Найду корень уравнения: cos(x)=8/17

Вы ввели

cos(x) = 8/17

$$\cos{\left(x \right)} = \frac{8}{17}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{8}{17}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{8}{17} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{8}{17} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{8}{17} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{8}{17} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(8/17) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(\frac{8}{17} \right)} + 2 \pi$$

x2 = acos(8/17)

$$x_{2} = \operatorname{acos}{\left(\frac{8}{17} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(8/17) + 2*pi + acos(8/17)

$$\operatorname{acos}{\left(\frac{8}{17} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{8}{17} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(8/17) + 2*pi)*acos(8/17)

$$1 \left(- \operatorname{acos}{\left(\frac{8}{17} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{8}{17} \right)}$$

=

(-acos(8/17) + 2*pi)*acos(8/17)

$$\left(- \operatorname{acos}{\left(\frac{8}{17} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{8}{17} \right)}$$

Численный ответ

x1 = -68.0341993784343

x2 = 49.1846434568955

x3 = 93.1669406071526

x4 = 7.36402430772076

x5 = 38.7799508436187

x6 = -95.328618608235

x7 = 86.883755299973

x8 = -82.7622479938758

x9 = -99.4501259143322

x10 = 45.0631361507983

x11 = -93.1669406071526

x12 = -49.1846434568955

x13 = -36.6182728425363

x14 = -86.883755299973

x15 = 80.6005699927935

x16 = -63.912692072337

x17 = -80.6005699927935

x18 = 95.328618608235

x19 = -57.6295067651574

x20 = -38.7799508436187

x21 = -1.08083900054117

x22 = 61.7510140712547

x23 = 76.4790626866962

x24 = -32.4967655364391

x25 = -76.4790626866962

x26 = 42.9014581497159

x27 = 89.0454333010554

x28 = -89.0454333010554

x29 = 26.2135802292595

x30 = 11.485531613818

x31 = 32.4967655364391

x32 = -45.0631361507983

x33 = -24.0519022281772

x34 = 51.3463214579779

x35 = -61.7510140712547

x36 = -55.4678287640751

x37 = 63.912692072337

x38 = 55.4678287640751

x39 = -70.1958773795166

x40 = 5.20234630663842

x41 = 57.6295067651574

x42 = 36.6182728425363

x43 = 99.4501259143322

x44 = -13.6472096149003

x45 = -51.3463214579779

x46 = -7.36402430772076

x47 = 68.0341993784343

x48 = 70.1958773795166

x49 = -30.3350875353568

x50 = 30.3350875353568

x51 = -74.3173846856139

x52 = -5.20234630663842

x53 = -11.485531613818

x54 = -193.697905522026

x55 = 74.3173846856139

x56 = -19.9303949220799

x57 = -26.2135802292595

x58 = -42.9014581497159

x59 = 13.6472096149003

x60 = 1.08083900054117

x61 = 24.0519022281772

x62 = 19.9303949220799

x63 = 82.7622479938758

x64 = 17.7687169209976

x65 = -17.7687169209976

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