sin((10*pi/9)-3*x)=1

Разделим обе части ур-ния на -1

Ур-ние превратится в
$$cos{left (3 x + frac{7 pi}{18} right )} = -1$$
Это ур-ние преобразуется в
$$3 x + frac{7 pi}{18} = pi n + {acos}{left (-1 right )}$$
$$3 x + frac{7 pi}{18} = pi n – pi + {acos}{left (-1 right )}$$
Или
$$3 x + frac{7 pi}{18} = pi n + pi$$
$$3 x + frac{7 pi}{18} = pi n$$
, где n – любое целое число
Перенесём
$$frac{7 pi}{18}$$
в правую часть ур-ния
с противоположным знаком, итого:
$$3 x = pi n + frac{11 pi}{18}$$
$$3 x = pi n – frac{7 pi}{18}$$
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = frac{pi n}{3} + frac{11 pi}{54}$$
$$x_{2} = frac{pi n}{3} – frac{7 pi}{54}$$

11*pi
x1 = —–
54

x1 = -11.9264168129000

x2 = 17.3951149687000

x3 = 40.4334609036000

x4 = -68.4750841558000

x5 = 86.5101531275000

x6 = 61.3774120937000

x7 = -47.5311334111000

x8 = -18.2096017338000

x9 = 94.8877336291000

x10 = 52.9998319591000

x11 = 36.2446708038000

x12 = -70.5694792972000

x13 = 42.5278559716000

x14 = 25.7726954226000

x15 = -7155.90811085000

x16 = 96.9821291555000

x17 = -55.9087134637000

x18 = -37.0591576500000

x19 = 32.0558804686000

x20 = 67.6605974984000

x21 = 34.1502758190000

x22 = 29.9614855301000

x23 = -58.0031088043000

x24 = 59.2830166407000

x25 = -51.7199235216000

x26 = 44.6222510522000

x27 = 88.6045482054000

x28 = -166.911654507000

x29 = -28.6815774049000

x30 = -99.8910103310000

x31 = 46.7166461507000

x32 = 23.6783003451000

x33 = 15.3007195986000

x34 = -3.54883625390000

x35 = -20.3039968087000

x36 = -28.6815774669000

x37 = 27.8670904862000

x38 = 6.92313942599000

x39 = -45.4367383387000

x40 = 50.9054365206000

x41 = -78.9470599486000

x42 = -74.7582691038000

x43 = 84.4157577967000

x44 = 21.5839052520000

x45 = -66.3806890499000

x46 = -22.3983918986000

x47 = 19.4895101360000

x48 = -89.4190354932000

x49 = -14.0208116356000

x50 = -16.1152066731000

x51 = 92.7933384239000

x52 = 11.1119297305000

x53 = -1.45444118377000

x54 = 63.4718072796000

x55 = 4.82874414661000

x56 = 73.9437826931000

x57 = 82.3213630065000

x58 = -87.3246404036000

x59 = -5.64323131313000

x60 = -60.0975038331000

x61 = 69.7549925786000

x62 = -85.2302452892000

x63 = -39.1535529866000

x64 = 71.8493876449000

x65 = 73.9437826938000

x66 = -7.73762635942000

x67 = -26.5871822222000

x68 = -93.6078256311000

x69 = -24.4927870093000

x70 = 65.5662024018000

x71 = -64.2862939631000

x72 = -62.1918988907000

x73 = -26.5871821621000

x74 = 38.3390658465000

x75 = 48.8110412837000

x76 = -43.3423432524000

x77 = -91.5134305679000

x78 = 76.0381776799000

x79 = 2.73434900271000

x80 = 0.639953899553000

x81 = -9.83202136653000

x82 = 78.1325729964000

x83 = 80.2269679683000

x84 = -95.7022206830000

x85 = -41.2479481440000

x86 = -81.0414547025000

x87 = -97.7966157130000

x88 = 90.6989432998000

x89 = 84.4157580615000

x90 = -49.6255284723000

x91 = -72.6638745533000

x92 = -83.1358501147000

x93 = -53.8143185425000