cos((pi*(8*x+1)/6))=sqrt(3)/2

$$cos{left (frac{pi}{6} left(8 x + 1right) right )} = frac{sqrt{3}}{2}$$

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

$$x_{1} = 0$$

x2 = 5/4

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

x1 = 76.2500000000000

x2 = -12.0000000000000

x3 = 78.0000000000000

x4 = -25.7500000000000

x5 = 54.0000000000000

x6 = 88.2500000000000

x7 = -91.7500000000000

x8 = 64.2500000000000

x9 = -31.7500000000000

x10 = 34.2500000000000

x11 = 10.2500000000000

x12 = -43.7500000000000

x13 = -66.0000000000000

x14 = 94.2500000000000

x15 = 36.0000000000000

x16 = -7.75000000000000

x17 = -18.0000000000000

x18 = -67.7500000000000

x19 = 58.2500000000000

x20 = -60.0000000000000

x21 = 72.0000000000000

x22 = 96.0000000000000

x23 = 90.0000000000000

x24 = -78.0000000000000

x25 = -90.0000000000000

x26 = -73.7500000000000

x27 = -96.0000000000000

x28 = -48.0000000000000

x29 = 48.0000000000000

x30 = -55.7500000000000

x31 = 46.2500000000000

x32 = 66.0000000000000

x33 = 12.0000000000000

x34 = -54.0000000000000

x35 = -37.7500000000000

x36 = 24.0000000000000

x37 = 70.2500000000000

x38 = -85.7500000000000

x39 = 28.2500000000000

x40 = -24.0000000000000

x41 = 60.0000000000000

x42 = 6.00000000000000

x43 = 4.25000000000000

x44 = -42.0000000000000

x45 = -1.75000000000000

x46 = 40.2500000000000

x47 = 42.0000000000000

x48 = 84.0000000000000

x49 = 82.2500000000000

x50 = -6.00000000000000

x51 = -84.0000000000000

x52 = -79.7500000000000

x53 = 16.2500000000000

x54 = -97.7500000000000

x55 = -19.7500000000000

x56 = -1.81141085987000e-16

x57 = 52.2500000000000

x58 = 22.2500000000000

x59 = 100.250000000000

x60 = 30.0000000000000

x61 = -61.7500000000000

x62 = -49.7500000000000

x63 = -13.7500000000000

x64 = -72.0000000000000

x65 = 18.0000000000000

x66 = -36.0000000000000

x67 = -30.0000000000000