cos(x)=2/7 (уравнение)

Найду корень уравнения: cos(x)=2/7

Вы ввели

cos(x) = 2/7

$$\cos{\left(x \right)} = \frac{2}{7}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{2}{7}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{2}{7} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{2}{7} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{2}{7} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{2}{7} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(2/7) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(\frac{2}{7} \right)} + 2 \pi$$

x2 = acos(2/7)

$$x_{2} = \operatorname{acos}{\left(\frac{2}{7} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(2/7) + 2*pi + acos(2/7)

$$\operatorname{acos}{\left(\frac{2}{7} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{2}{7} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(2/7) + 2*pi)*acos(2/7)

$$1 \left(- \operatorname{acos}{\left(\frac{2}{7} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{2}{7} \right)}$$

=

(-acos(2/7) + 2*pi)*acos(2/7)

$$\left(- \operatorname{acos}{\left(\frac{2}{7} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{2}{7} \right)}$$

Численный ответ

x1 = 13.847415239718

x2 = 17.5685112961799

x3 = -48.9844378320778

x4 = 7.56422993253844

x5 = -7.56422993253844

x6 = -82.9624536186935

x7 = -38.9801564684364

x8 = -32.6969711612568

x9 = -55.2676231392574

x10 = 32.6969711612568

x11 = 23.8516966033595

x12 = -61.550808446437

x13 = -99.2499202895145

x14 = -23.8516966033595

x15 = 5.00214068182074

x16 = 26.4137858540772

x17 = -17.5685112961799

x18 = -64.1128976971547

x19 = 30.1348819105391

x20 = -30.1348819105391

x21 = -86.6835496751554

x22 = 57.8297123899751

x23 = 89.2456389258731

x24 = -11.2853259890003

x25 = 55.2676231392574

x26 = 67.8339937536166

x27 = -51.5465270827955

x28 = 45.263341775616

x29 = 36.4180672177187

x30 = 61.550808446437

x31 = -5.00214068182074

x32 = -70.3960830043343

x33 = 95.5288242330526

x34 = 11.2853259890003

x35 = 48.9844378320778

x36 = -57.8297123899751

x37 = -45.263341775616

x38 = -67.8339937536166

x39 = -74.1171790607962

x40 = 76.6792683115139

x41 = -80.4003643679758

x42 = -36.4180672177187

x43 = 80.4003643679758

x44 = 99.2499202895145

x45 = 74.1171790607962

x46 = -92.9667349823349

x47 = -95.5288242330526

x48 = -76.6792683115139

x49 = 20.1306005468976

x50 = -42.7012525248983

x51 = 1.28104462535885

x52 = 64.1128976971547

x53 = -13.847415239718

x54 = 86.6835496751554

x55 = 70.3960830043343

x56 = 82.9624536186935

x57 = -20.1306005468976

x58 = -1.28104462535885

x59 = 51.5465270827955

x60 = 828.099415922347

x61 = 1722.87381879257

x62 = -26.4137858540772

x63 = 42.7012525248983

x64 = -89.2456389258731

x65 = 38.9801564684364

x66 = 92.9667349823349

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