cosx=4/7 (уравнение)

Найду корень уравнения: cosx=4/7

Вы ввели

cos(x) = 4/7

$$\cos{\left(x \right)} = \frac{4}{7}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{4}{7}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{4}{7} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{4}{7} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{4}{7} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{4}{7} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(4/7) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(\frac{4}{7} \right)} + 2 \pi$$

x2 = acos(4/7)

$$x_{2} = \operatorname{acos}{\left(\frac{4}{7} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(4/7) + 2*pi + acos(4/7)

$$\operatorname{acos}{\left(\frac{4}{7} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{4}{7} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(4/7) + 2*pi)*acos(4/7)

$$1 \left(- \operatorname{acos}{\left(\frac{4}{7} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{4}{7} \right)}$$

=

(-acos(4/7) + 2*pi)*acos(4/7)

$$\left(- \operatorname{acos}{\left(\frac{4}{7} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{4}{7} \right)}$$

Численный ответ

x1 = 7.24573605506427

x2 = 30.4533757880132

x3 = -93.2852288598091

x4 = 49.302931709552

x5 = 70.0775891268601

x6 = -11.6038198664745

x7 = -88.9271450483989

x8 = 24.1701904808337

x9 = 55.5861170167316

x10 = -17.8870051736541

x11 = 80.7188582454499

x12 = 57.511218512501

x13 = 74.4356729382704

x14 = -99.5684141669887

x15 = -51.2280332053214

x16 = -57.511218512501

x17 = 38.6616625909622

x18 = -101.493515662758

x19 = 13.5289213622439

x20 = 44.9448478981418

x21 = -49.302931709552

x22 = 99.5684141669887

x23 = -70.0775891268601

x24 = 17.8870051736541

x25 = -43.0197464023724

x26 = 51.2280332053214

x27 = 95.2103303555785

x28 = 32.3784772837826

x29 = -82.6439597412193

x30 = 19.8121066694234

x31 = -55.5861170167316

x32 = 36.7365610951928

x33 = 63.7944038196806

x34 = -30.4533757880132

x35 = 76.3607744340397

x36 = 0.962550747884687

x37 = -76.3607744340397

x38 = -5.3206345592949

x39 = 93.2852288598091

x40 = -0.962550747884687

x41 = 61.8693023239112

x42 = -13.5289213622439

x43 = 43.0197464023724

x44 = -24.1701904808337

x45 = 5.3206345592949

x46 = -87.0020435526295

x47 = -7.24573605506427

x48 = -61.8693023239112

x49 = 88.9271450483989

x50 = 26.095291976603

x51 = -95.2103303555785

x52 = 68.1524876310908

x53 = -38.6616625909622

x54 = -26.095291976603

x55 = 11.6038198664745

x56 = -36.7365610951928

x57 = 87.0020435526295

x58 = -32.3784772837826

x59 = -80.7188582454499

x60 = -68.1524876310908

x61 = -74.4356729382704

x62 = -19.8121066694234

x63 = 82.6439597412193

x64 = -44.9448478981418

x65 = -63.7944038196806

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