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 = 70.0775891268601

x2 = 0.962550747884687

x3 = -68.1524876310908

x4 = -88.9271450483989

x5 = -19.8121066694234

x6 = 76.3607744340397

x7 = 24.1701904808337

x8 = -36.7365610951928

x9 = -101.493515662758

x10 = -70.0775891268601

x11 = 93.2852288598091

x12 = -57.511218512501

x13 = -44.9448478981418

x14 = 19.8121066694234

x15 = -26.095291976603

x16 = -76.3607744340397

x17 = -30.4533757880132

x18 = -43.0197464023724

x19 = -32.3784772837826

x20 = 51.2280332053214

x21 = 80.7188582454499

x22 = 55.5861170167316

x23 = -13.5289213622439

x24 = 49.302931709552

x25 = 82.6439597412193

x26 = 43.0197464023724

x27 = 32.3784772837826

x28 = 30.4533757880132

x29 = 57.511218512501

x30 = -49.302931709552

x31 = -74.4356729382704

x32 = -61.8693023239112

x33 = 26.095291976603

x34 = 87.0020435526295

x35 = 11.6038198664745

x36 = 68.1524876310908

x37 = -87.0020435526295

x38 = 5.3206345592949

x39 = -55.5861170167316

x40 = 74.4356729382704

x41 = 7.24573605506427

x42 = -38.6616625909622

x43 = 13.5289213622439

x44 = -93.2852288598091

x45 = -99.5684141669887

x46 = -63.7944038196806

x47 = -95.2103303555785

x48 = 88.9271450483989

x49 = 95.2103303555785

x50 = -24.1701904808337

x51 = -51.2280332053214

x52 = 17.8870051736541

x53 = 63.7944038196806

x54 = -5.3206345592949

x55 = -17.8870051736541

x56 = -82.6439597412193

x57 = -7.24573605506427

x58 = 61.8693023239112

x59 = 36.7365610951928

x60 = -0.962550747884687

x61 = 44.9448478981418

x62 = -80.7188582454499

x63 = 38.6616625909622

x64 = 99.5684141669887

x65 = -11.6038198664745

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