sin(3*x)=-1/2

$$sin{left (3 x right )} = – frac{1}{2}$$

Дано уравнение
$$sin{left (3 x right )} = – frac{1}{2}$$
– это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$3 x = 2 pi n + {asin}{left (- frac{1}{2} right )}$$
$$3 x = 2 pi n – {asin}{left (- frac{1}{2} right )} + pi$$
Или
$$3 x = 2 pi n – frac{pi}{6}$$
$$3 x = 2 pi n + frac{7 pi}{6}$$
, где n – любое целое число
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = frac{2 pi}{3} n – frac{pi}{18}$$
$$x_{2} = frac{2 pi}{3} n + frac{7 pi}{18}$$

-pi
x1 = —-
18

$$x_{1} = – frac{pi}{18}$$

7*pi
x2 = —-
18

$$x_{2} = frac{7 pi}{18}$$

x1 = -17.6278254451000

x2 = 6.10865238198000

x3 = -28.0998009571000

x4 = 56.3741348394000

x5 = -26.0054058547000

x6 = 12.3918376892000

x7 = 74.5255590602000

x8 = 85.6956662729000

x9 = -21.8166156499000

x10 = -72.0820981074000

x11 = 8.20304748437000

x12 = 68.2423737530000

x13 = 96.1676417849000

x14 = -44.1568300755000

x15 = -51.1381470834000

x16 = 52.1853446346000

x17 = 64.0535835482000

x18 = 28.4488668075000

x19 = -79.7615468161000

x20 = 45.9021593275000

x21 = -46.2512251778000

x22 = -19.7222205475000

x23 = 89.8844564777000

x24 = 83.6012711705000

x25 = 50.0909495322000

x26 = 32.6376570123000

x27 = -61.6101225954000

x28 = -11.3446401380000

x29 = 47.9965544298000

x30 = -33.6848545635000

x31 = -67.8933079026000

x32 = 30.5432619099000

x33 = 98.2620368873000

x34 = -65.7989128002000

x35 = -69.9877030050000

x36 = 91.9788515801000

x37 = 10.2974425868000

x38 = 24.2600766027000

x39 = 4.01425727959000

x40 = -75.5727566114000

x41 = -13.4390352404000

x42 = 43.8077642251000

x43 = -54.6288055874000

x44 = 26.3544717051000

x45 = 87.7900613753000

x46 = -23.9110107523000

x47 = 1.91986217719000

x48 = 61.9591884458000

x49 = 54.2797397370000

x50 = 70.3367688554000

x51 = -48.3456202802000

x52 = 94.0732466825000

x53 = -59.5157274930000

x54 = -15.5334303427000

x55 = 66.1479786506000

x56 = -2.26892802759000

x57 = 646.295422014000

x58 = 15.8824961931000

x59 = -0.174532925199000

x60 = -63.7045176978000

x61 = 33.3357887131000

x62 = 72.4311639578000

x63 = -88.1391272257000

x64 = -74.1764932098000

x65 = -57.4213323906000

x66 = 20.0712863979000

x67 = 59.8647933434000

x68 = -42.0624349731000

x69 = -90.2335223281000

x70 = 39.6189740203000

x71 = -31.5904594611000

x72 = -98.6111027377000

x73 = 17.9768912955000

x74 = 41.7133691227000

x75 = -39.9680398707000

x76 = -83.9503370209000

x77 = 100.356431990000

x78 = -7.15584993318000

x79 = 76.6199541626000

x80 = 77.3180858633000

x81 = -92.3279174305000

x82 = -37.8736447683000

x83 = -16.9296937443000

x84 = -81.8559419185000

x85 = -35.7792496659000

x86 = 22.1656815003000

x87 = -4.36332312999000

x88 = -77.6671517137000

x89 = -86.0447321233000