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

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

$$\operatorname{acos}{\left(\frac{3}{8} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{3}{8} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

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

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

=

(-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 = -7281.02537146884

x2 = 32.6023260881972

x3 = 86.778194748215

x4 = -36.5127122907783

x5 = -20.035955473838

x6 = -70.3014379312747

x7 = -55.362268212317

x8 = -67.9286388266762

x9 = 36.5127122907783

x10 = 70.3014379312747

x11 = -89.1509938528135

x12 = -1.18639955229926

x13 = 61.6454535194966

x14 = -45.1686967025564

x15 = 67.9286388266762

x16 = 64.0182526240951

x17 = 23.9463416764191

x18 = 82.8678085456339

x19 = -13.7527701666584

x20 = 13.7527701666584

x21 = 57.7350673169155

x22 = -42.7958975979578

x23 = 89.1509938528135

x24 = 80.4950094410354

x25 = 1.18639955229926

x26 = 20.035955473838

x27 = 26.3191407810176

x28 = -95.4341791599931

x29 = 105.627750669754

x30 = -11.3799710620599

x31 = -76.5846232384543

x32 = -5.09678575488033

x33 = -80.4950094410354

x34 = 76.5846232384543

x35 = -17.6631563692395

x36 = 30.2295269835987

x37 = 17.6631563692395

x38 = -30.2295269835987

x39 = 45.1686967025564

x40 = 55.362268212317

x41 = 7.46958485947884

x42 = -82.8678085456339

x43 = 42.7958975979578

x44 = -26.3191407810176

x45 = -64.0182526240951

x46 = 49.0790829051374

x47 = -74.2118241338558

x48 = -7.46958485947884

x49 = -23.9463416764191

x50 = -57.7350673169155

x51 = 93.0613800553945

x52 = 11.3799710620599

x53 = 51.4518820097359

x54 = -51.4518820097359

x55 = -49.0790829051374

x56 = -93.0613800553945

x57 = -61.6454535194966

x58 = 5.09678575488033

x59 = -86.778194748215

x60 = -38.8855113953768

x61 = 38.8855113953768

x62 = 74.2118241338558

x63 = -32.6023260881972

x64 = 99.3445653625741

x65 = 95.4341791599931

x66 = -99.3445653625741

График