cos(x)=(2/5) (уравнение)

Найду корень уравнения: cos(x)=(2/5)

Вы ввели

cos(x) = 2/5

$$\cos{\left(x \right)} = \frac{2}{5}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{2}{5}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{2}{5} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{2}{5} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{2}{5} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{2}{5} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(2/5) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(\frac{2}{5} \right)} + 2 \pi$$

x2 = acos(2/5)

$$x_{2} = \operatorname{acos}{\left(\frac{2}{5} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(2/5) + 2*pi + acos(2/5)

$$\operatorname{acos}{\left(\frac{2}{5} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{2}{5} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(2/5) + 2*pi)*acos(2/5)

$$1 \left(- \operatorname{acos}{\left(\frac{2}{5} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{2}{5} \right)}$$

=

(-acos(2/5) + 2*pi)*acos(2/5)

$$\left(- \operatorname{acos}{\left(\frac{2}{5} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{2}{5} \right)}$$

Численный ответ

x1 = -80.5221295126072

x2 = -17.6902764408113

x3 = -93.0885001269664

x4 = -20.0088354022662

x5 = -74.2389442054276

x6 = 80.5221295126072

x7 = -30.2566470551705

x8 = 70.2743178597029

x9 = -99.371685434146

x10 = -57.7079472453437

x11 = 55.3893882838889

x12 = 6070.71628621621

x13 = -89.1238737812416

x14 = 7.44246478790699

x15 = -7.44246478790699

x16 = 11.4070911336318

x17 = -23.9734617479909

x18 = 51.4247619381641

x19 = 23.9734617479909

x20 = 26.2920207094458

x21 = -70.2743178597029

x22 = 38.8583913238049

x23 = -36.5398323623501

x24 = -1.15927948072741

x25 = -55.3893882838889

x26 = -82.840688474062

x27 = -51.4247619381641

x28 = 17.6902764408113

x29 = 95.4070590884212

x30 = -26.2920207094458

x31 = 61.6725735910685

x32 = -61.6725735910685

x33 = -13.7256500950866

x34 = 49.1062029767093

x35 = 42.8230176695297

x36 = 13.7256500950866

x37 = -95.4070590884212

x38 = 89.1238737812416

x39 = -32.5752060166253

x40 = 30.2566470551705

x41 = -86.8053148197868

x42 = 143.353982584403

x43 = 82.840688474062

x44 = 74.2389442054276

x45 = -63.9911325525233

x46 = -11.4070911336318

x47 = -49.1062029767093

x48 = -5.12390582645218

x49 = 63.9911325525233

x50 = 93.0885001269664

x51 = -45.1415766309845

x52 = 32.5752060166253

x53 = 67.955758898248

x54 = 1.15927948072741

x55 = 45.1415766309845

x56 = -67.955758898248

x57 = 76.5575031668824

x58 = 57.7079472453437

x59 = 5.12390582645218

x60 = 99.371685434146

x61 = 36.5398323623501

x62 = 86.8053148197868

x63 = -76.5575031668824

x64 = 20.0088354022662

x65 = -42.8230176695297

x66 = -38.8583913238049

График