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 = -67.1327252061131

x2 = -64.8141662446583

x3 = 20.8318690944011

x4 = 39.6814250159399

x5 = 58.5309809374787

x6 = -10.5840574414968

x7 = -29.4336133630355

x8 = 27.1150544015807

x9 = -8.26549848004197

x10 = 85.9822811276518

x11 = 83.663722166197

x12 = 29.4336133630355

x13 = -54.5663545917539

x14 = 10.5840574414968

x15 = 64.8141662446583

x16 = 8.26549848004197

x17 = -39.6814250159399

x18 = -35.7167986702151

x19 = -14.5486837872216

x20 = -5822.53046658261

x21 = 35.7167986702151

x22 = -48.2831692845743

x23 = -58.5309809374787

x24 = -89.9469074733766

x25 = -52.2477956302991

x26 = -27.1150544015807

x27 = 89.9469074733766

x28 = 92.2654664348314

x29 = -16.8672427486764

x30 = 96.2300927805562

x31 = 33.3982397087603

x32 = -83.663722166197

x33 = 60.8495398989335

x34 = 54.5663545917539

x35 = -45.9646103231195

x36 = -60.8495398989335

x37 = 14.5486837872216

x38 = 98.548651742011

x39 = 1.98231317286238

x40 = -73.4159105132927

x41 = 67.1327252061131

x42 = 45.9646103231195

x43 = 16.8672427486764

x44 = 4.3008721343172

x45 = -20.8318690944011

x46 = 41.9999839773947

x47 = 23.150428055856

x48 = 73.4159105132927

x49 = -96.2300927805562

x50 = -85.9822811276518

x51 = 79.6990958204722

x52 = -79.6990958204722

x53 = -1.98231317286238

x54 = -33.3982397087603

x55 = -41.9999839773947

x56 = -98.548651742011

x57 = 71.0973515518378

x58 = -92.2654664348314

x59 = 77.3805368590174

x60 = -77.3805368590174

x61 = -23.150428055856

x62 = 52.2477956302991

x63 = -4.3008721343172

x64 = 48.2831692845743

x65 = -71.0973515518378

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