cos(pi*(4*x-6)/3)=1/2

$$cos{left (frac{pi}{3} left(4 x – 6right) right )} = frac{1}{2}$$

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

$$x_{1} = frac{1}{4}$$

x2 = 5/4

$$x_{2} = frac{5}{4}$$

x1 = 76.2500000000000

x2 = 7.75000000000000

x3 = 88.2500000000000

x4 = -31.7500000000000

x5 = -16.2500000000000

x6 = 60.2500000000000

x7 = 0.250000000000000

x8 = -22.2500000000000

x9 = -53.7500000000000

x10 = 24.2500000000000

x11 = -85.7500000000000

x12 = -73.7500000000000

x13 = -46.2500000000000

x14 = -71.7500000000000

x15 = 4.25000000000000

x16 = 1.75000000000000

x17 = 54.2500000000000

x18 = 48.2500000000000

x19 = -10.2500000000000

x20 = -29.7500000000000

x21 = 78.2500000000000

x22 = 22.2500000000000

x23 = 42.2500000000000

x24 = -13.7500000000000

x25 = -100.250000000000

x26 = 37.7500000000000

x27 = 94.2500000000000

x28 = -95.7500000000000

x29 = 6.25000000000000

x30 = -35.7500000000000

x31 = 70.2500000000000

x32 = -7.75000000000000

x33 = 31.7500000000000

x34 = -4.25000000000000

x35 = -67.7500000000000

x36 = -52.2500000000000

x37 = 46.2500000000000

x38 = -47.7500000000000

x39 = -70.2500000000000

x40 = 28.2500000000000

x41 = 18.2500000000000

x42 = -1.75000000000000

x43 = 82.2500000000000

x44 = 64.2500000000000

x45 = -41.7500000000000

x46 = 52.2500000000000

x47 = 61.7500000000000

x48 = -49.7500000000000

x49 = -61.7500000000000

x50 = 12.2500000000000

x51 = -94.2500000000000

x52 = 66.2500000000000

x53 = 96.2500000000000

x54 = -82.2500000000000

x55 = -5.75000000000000

x56 = 10.2500000000000

x57 = -25.7500000000000

x58 = -88.2500000000000

x59 = 72.2500000000000

x60 = -11.7500000000000

x61 = -64.2500000000000

x62 = -19.7500000000000

x63 = -91.7500000000000

x64 = 79.7500000000000

x65 = 67.7500000000000

x66 = 16.2500000000000

x67 = -34.2500000000000

x68 = 34.2500000000000

x69 = -77.7500000000000

x70 = 85.7500000000000

x71 = 25.7500000000000

x72 = -59.7500000000000

x73 = 97.7500000000000

x74 = -83.7500000000000

x75 = 30.2500000000000

x76 = -43.7500000000000

x77 = -17.7500000000000

x78 = -89.7500000000000

x79 = 73.7500000000000

x80 = 19.7500000000000

x81 = 58.2500000000000

x82 = -65.7500000000000

x83 = -55.7500000000000

x84 = 13.7500000000000

x85 = 36.2500000000000

x86 = -37.7500000000000

x87 = -40.2500000000000

x88 = 40.2500000000000

x89 = 55.7500000000000

x90 = -23.7500000000000

x91 = 49.7500000000000

x92 = 90.2500000000000

x93 = -97.7500000000000

x94 = -28.2500000000000

x95 = -76.2500000000000

x96 = 100.250000000000

x97 = 84.2500000000000

x98 = 43.7500000000000

x99 = 91.7500000000000

x100 = -79.7500000000000

x101 = -58.2500000000000