2*cos(3*x)+1=0

Перенесём 1 в правую часть ур-ния

с изменением знака при 1

Получим:
$$2 cos{left (3 x right )} = -1$$

Разделим обе части ур-ния на 2

Ур-ние превратится в
$$cos{left (3 x right )} = – frac{1}{2}$$
Это ур-ние преобразуется в
$$3 x = pi n + {acos}{left (- frac{1}{2} right )}$$
$$3 x = pi n – pi + {acos}{left (- frac{1}{2} right )}$$
Или
$$3 x = pi n + frac{2 pi}{3}$$
$$3 x = pi n – frac{pi}{3}$$
, где n – любое целое число
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = frac{pi n}{3} + frac{2 pi}{9}$$
$$x_{2} = frac{pi n}{3} – frac{pi}{9}$$

2*pi
x1 = —-
9

4*pi
x2 = —-
9

x1 = 60.0393262686000

x2 = 6.98131700798000

x3 = -49.5673507566000

x4 = 95.6440430093000

x5 = -23.7364778271000

x6 = 82.3795406941000

x7 = -80.2851455917000

x8 = -65.6243798750000

x9 = 27.9252680319000

x10 = -74.0019602846000

x11 = -51.6617458590000

x12 = 36.3028484415000

x13 = -247.836753783000

x14 = -27.9252680319000

x15 = -67.7187749774000

x16 = 49.5673507566000

x17 = 32.1140582367000

x18 = 86.5683308989000

x19 = -99.8328332141000

x20 = -93.5496479069000

x21 = -53.7561409614000

x22 = -95.6440430093000

x23 = -60.0393262686000

x24 = 99.8328332141000

x25 = 92.8515162061000

x26 = 88.6627260013000

x27 = 45.3785605519000

x28 = 42.5860337487000

x29 = 80.2851455917000

x30 = -3.49065850399000

x31 = 38.3972435439000

x32 = 24.4346095279000

x33 = -78.1907504893000

x34 = 62.1337213710000

x35 = -11.8682389136000

x36 = 68.4169066782000

x37 = -5.58505360638000

x38 = -69.8131700798000

x39 = -41.1897703471000

x40 = -25.8308729295000

x41 = -7.67944870878000

x42 = 84.4739357965000

x43 = -47.4729556542000

x44 = -57.9449311662000

x45 = -13.9626340160000

x46 = 11.8682389136000

x47 = -18.1514242207000

x48 = 78.1907504893000

x49 = 57.9449311662000

x50 = 74.0019602846000

x51 = 22.3402144255000

x52 = 34.2084533391000

x53 = 55.8505360638000

x54 = -62.1337213710000

x55 = -9.77384381117000

x56 = -45.3785605519000

x57 = 25.8308729295000

x58 = 76.0963553870000

x59 = -21.6420827247000

x60 = 20.2458193231000

x61 = 66.3225115758000

x62 = 71.9075651822000

x63 = 87.2664625997000

x64 = -82.3795406941000

x65 = 1.39626340160000

x66 = -71.9075651822000

x67 = 48.8692190558000

x68 = -55.8505360638000

x69 = 53.7561409614000

x70 = -38.3972435439000

x71 = 18.1514242207000

x72 = -16.0570291183000

x73 = -34.2084533391000

x74 = 7.67944870878000

x75 = 13.9626340160000

x76 = -97.7384381117000

x77 = 4.88692190558000

x78 = 69.8131700798000

x79 = -1.39626340160000

x80 = 9.77384381117000

x81 = -76.0963553870000

x82 = 40.4916386463000

x83 = -30.0196631343000

x84 = 64.2281164734000

x85 = -32.1140582367000

x86 = 44.6804288511000

x87 = -36.3028484415000

x88 = 16.0570291183000

x89 = -89.3608577021000

x90 = 97.7384381117000

x91 = -91.4552528045000

x92 = 30.0196631343000

x93 = 51.6617458590000