cos(x)=(3/8) (уравнение)

Найду корень уравнения: cos(x)=(3/8)

Вы ввели

cos(x) = 3/8

$$\cos{\left(x \right)} = \frac{3}{8}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{3}{8}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{3}{8} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{3}{8} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{3}{8} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{3}{8} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(3/8) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(\frac{3}{8} \right)} + 2 \pi$$

x2 = acos(3/8)

$$x_{2} = \operatorname{acos}{\left(\frac{3}{8} \right)}$$

Сумма и произведение корней

сумма

-acos(3/8) + 2*pi + acos(3/8)

$$\operatorname{acos}{\left(\frac{3}{8} \right)} + \left(- \operatorname{acos}{\left(\frac{3}{8} \right)} + 2 \pi\right)$$

=

2*pi

$$2 \pi$$

произведение

(-acos(3/8) + 2*pi)*acos(3/8)

$$\left(- \operatorname{acos}{\left(\frac{3}{8} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{3}{8} \right)}$$

=

(-acos(3/8) + 2*pi)*acos(3/8)

$$\left(- \operatorname{acos}{\left(\frac{3}{8} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{3}{8} \right)}$$

Численный ответ

x1 = 13.7527701666584

x2 = -49.0790829051374

x3 = 38.8855113953768

x4 = 93.0613800553945

x5 = 80.4950094410354

x6 = 51.4518820097359

x7 = 89.1509938528135

x8 = 55.362268212317

x9 = -93.0613800553945

x10 = 17.6631563692395

x11 = 5.09678575488033

x12 = -64.0182526240951

x13 = 7.46958485947884

x14 = 42.7958975979578

x15 = 49.0790829051374

x16 = 23.9463416764191

x17 = -23.9463416764191

x18 = 36.5127122907783

x19 = -30.2295269835987

x20 = 11.3799710620599

x21 = -7.46958485947884

x22 = -36.5127122907783

x23 = -86.778194748215

x24 = -13.7527701666584

x25 = -55.362268212317

x26 = 95.4341791599931

x27 = 67.9286388266762

x28 = -38.8855113953768

x29 = -74.2118241338558

x30 = -11.3799710620599

x31 = 64.0182526240951

x32 = -61.6454535194966

x33 = -32.6023260881972

x34 = 26.3191407810176

x35 = -42.7958975979578

x36 = 61.6454535194966

x37 = -7281.02537146884

x38 = 30.2295269835987

x39 = -57.7350673169155

x40 = -76.5846232384543

x41 = -45.1686967025564

x42 = 99.3445653625741

x43 = 74.2118241338558

x44 = 32.6023260881972

x45 = -80.4950094410354

x46 = 57.7350673169155

x47 = -95.4341791599931

x48 = -70.3014379312747

x49 = -20.035955473838

x50 = 1.18639955229926

x51 = 45.1686967025564

x52 = 76.5846232384543

x53 = -89.1509938528135

x54 = -99.3445653625741

x55 = -17.6631563692395

x56 = -82.8678085456339

x57 = 82.8678085456339

x58 = -1.18639955229926

x59 = -5.09678575488033

x60 = -51.4518820097359

x61 = 86.778194748215

x62 = 105.627750669754

x63 = -67.9286388266762

x64 = 70.3014379312747

x65 = -26.3191407810176

x66 = 20.035955473838

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