cos(8*pi*x/6)=sqrt(3)/2

$$cos{left (frac{8 pi}{6} x right )} = frac{sqrt{3}}{2}$$

Дано уравнение
$$cos{left (frac{8 pi}{6} x right )} = frac{sqrt{3}}{2}$$
– это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$frac{4 pi}{3} x = pi n + {acos}{left (frac{sqrt{3}}{2} right )}$$
$$frac{4 pi}{3} x = pi n – pi + {acos}{left (frac{sqrt{3}}{2} right )}$$
Или
$$frac{4 pi}{3} x = pi n + frac{pi}{6}$$
$$frac{4 pi}{3} x = pi n – frac{5 pi}{6}$$
, где n – любое целое число
Разделим обе части полученного ур-ния на
$$frac{4 pi}{3}$$
получим ответ:
$$x_{1} = frac{1}{4 pi} left(3 pi n + frac{pi}{2}right)$$
$$x_{2} = frac{1}{4 pi} left(3 pi n – frac{5 pi}{2}right)$$

$$x_{1} = frac{1}{8}$$

x2 = 11/8

$$x_{2} = frac{11}{8}$$

x1 = 43.3750000000000

x2 = -67.6250000000000

x3 = 36.1250000000000

x4 = 58.3750000000000

x5 = -37.6250000000000

x6 = -46.6250000000000

x7 = 31.3750000000000

x8 = 18.1250000000000

x9 = 84.1250000000000

x10 = 61.3750000000000

x11 = -17.8750000000000

x12 = 73.3750000000000

x13 = -35.8750000000000

x14 = -7.62500000000000

x15 = 4.37500000000000

x16 = -65.8750000000000

x17 = -58.6250000000000

x18 = 88.3750000000000

x19 = 100.375000000000

x20 = -89.8750000000000

x21 = -4.62500000000000

x22 = 79.3750000000000

x23 = 49.3750000000000

x24 = 85.3750000000000

x25 = 60.1250000000000

x26 = -79.6250000000000

x27 = -64.6250000000000

x28 = -83.8750000000000

x29 = 24.1250000000000

x30 = 52.3750000000000

x31 = 91.3750000000000

x32 = 25.3750000000000

x33 = 7.37500000000000

x34 = 70.3750000000000

x35 = -11.8750000000000

x36 = 78.1250000000000

x37 = 42.1250000000000

x38 = 16.3750000000000

x39 = 6.12500000000000

x40 = -34.6250000000000

x41 = -82.6250000000000

x42 = 82.3750000000000

x43 = 10.3750000000000

x44 = -100.625000000000

x45 = -52.6250000000000

x46 = -70.6250000000000

x47 = -97.6250000000000

x48 = 55.3750000000000

x49 = 48.1250000000000

x50 = 72.1250000000000

x51 = 94.3750000000000

x52 = 67.3750000000000

x53 = -91.6250000000000

x54 = 13.3750000000000

x55 = 76.3750000000000

x56 = 1.37500000000000

x57 = -10.6250000000000

x58 = -43.6250000000000

x59 = -31.6250000000000

x60 = 40.3750000000000

x61 = -40.6250000000000

x62 = 54.1250000000000

x63 = 46.3750000000000

x64 = -47.8750000000000

x65 = -16.6250000000000

x66 = 90.1250000000000

x67 = -85.6250000000000

x68 = -94.6250000000000

x69 = -53.8750000000000

x70 = -71.8750000000000

x71 = -61.6250000000000

x72 = -88.6250000000000

x73 = -95.8750000000000

x74 = -1.62500000000000

x75 = 37.3750000000000

x76 = 66.1250000000000

x77 = -73.6250000000000

x78 = 0.125000000000000

x79 = -29.8750000000000

x80 = 96.1250000000000

x81 = 64.3750000000000

x82 = -5.87500000000000

x83 = -25.6250000000000

x84 = -77.8750000000000

x85 = 30.1250000000000

x86 = 12.1250000000000

x87 = -49.6250000000000

x88 = -22.6250000000000

x89 = -41.8750000000000

x90 = -28.6250000000000

x91 = 22.3750000000000

x92 = -19.6250000000000

x93 = -55.6250000000000

x94 = -59.8750000000000

x95 = -23.8750000000000

x96 = 28.3750000000000

x97 = -13.6250000000000

x98 = 19.3750000000000

x99 = 97.3750000000000

x100 = -76.6250000000000

x101 = 34.3750000000000