2*sin(5*x)=2 (уравнение)

Найду корень уравнения: 2*sin(5*x)=2

Вы ввели

2*sin(5*x) = 2

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

Подробное решение

Дано уравнение
$$2 \sin{\left (5 x \right )} = 2$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 2

Ур-ние превратится в
$$\sin{\left (5 x \right )} = 1$$
Это ур-ние преобразуется в
$$5 x = 2 \pi n + \operatorname{asin}{\left (1 \right )}$$
$$5 x = 2 \pi n - \operatorname{asin}{\left (1 \right )} + \pi$$
Или
$$5 x = 2 \pi n + \frac{\pi}{2}$$
$$5 x = 2 \pi n + \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$5$$
получим ответ:
$$x_{1} = \frac{2 \pi}{5} n + \frac{\pi}{10}$$
$$x_{2} = \frac{2 \pi}{5} n + \frac{\pi}{10}$$

Быстрый ответ

     pi
x1 = --
     10

$$x_{1} = \frac{\pi}{10}$$

Численный ответ

x1 = -33.6150414656000

x2 = 44.2964563850000

x3 = 81.9955682639000

x4 = 71.9424718165000

x5 = -97.7035315573000

x6 = -90.1637090664000

x7 = 29.2168117490000

x8 = 31.7300858869000

x9 = -49.9513232903000

x10 = 95.8185760288000

x11 = -76.3407014732000

x12 = -91.4203462510000

x13 = 74.4557458009000

x14 = 48.0663674154000

x15 = 50.5796416912000

x16 = 85.7654795375000

x17 = 60.6327383914000

x18 = 94.5619388168000

x19 = 78.2256570939000

x20 = 71.9424718169000

x21 = -13.5088485002000

x22 = 92.0486646520000

x23 = -80.1106125902000

x24 = 10.3672556913000

x25 = -63.7743308484000

x26 = 64.4026493206000

x27 = -9.73893723410000

x28 = -19.7920336818000

x29 = -36.1283154337000

x30 = -46.1814119134000

x31 = -67.5442421414000

x32 = -47.4380491254000

x33 = -53.7212343962000

x34 = 17.9070781943000

x35 = -66.2876049140000

x36 = -16.0221225103000

x37 = 88.2787535461000

x38 = -37.3849525045000

x39 = 98.3318500076000

x40 = -3.45575199070000

x41 = 75.7123830283000

x42 = -100.216805554000

x43 = 14.1371670477000

x44 = -34.8716784592000

x45 = 30.4734486495000

x46 = -26.0752189648000

x47 = 27.9601746545000

x48 = -60.0044196784000

x49 = -56.2345084047000

x50 = 40.5265451499000

x51 = -29.8451301031000

x52 = 11.6238926856000

x53 = -53.7212346027000

x54 = 68.1725606608000

x55 = 16.6504412743000

x56 = -87.6504350932000

x57 = 6.59734458066000

x58 = -12.2522112577000

x59 = 7.85398172163000

x60 = -23.5619449885000

x61 = 17.9070782948000

x62 = 34.2433599292000

x63 = 51.8362788758000

x64 = 54.3495528491000

x65 = 41.7831823887000

x66 = 88.2787533397000

x67 = 0.314159224755000

x68 = -32.3584043769000

x69 = 21.6769893520000

x70 = 65.6592864691000

x71 = -81.3672495508000

x72 = -5.96902609117000

x73 = -93.9336205269000

x74 = -22.3053077773000

x75 = -77.5973386217000

x76 = -43.6681379346000

x77 = 38.0132710907000

x78 = 84.5088422945000

x79 = 24.1902634875000

x80 = 20.4203521655000

x81 = -70.0575161254000

x82 = 61.8893753520000

x83 = -2.19911476168000

x84 = -73.8274272815000

x85 = -57.4911456477000