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

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

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

$$x_{1} = 0$$

x2 = 2

$$x_{2} = 2$$

x1 = -12.0000000000000

x2 = 78.0000000000000

x3 = 6.00000000000000

x4 = 32.0000000000000

x5 = 92.0000000000000

x6 = -100.000000000000

x7 = 60.0000000000000

x8 = 12.0000000000000

x9 = -6.00000000000000

x10 = -66.0000000000000

x11 = 66.0000000000000

x12 = 80.0000000000000

x13 = 20.0000000000000

x14 = -10.0000000000000

x15 = 2.00000000000000

x16 = -82.0000000000000

x17 = -60.0000000000000

x18 = 54.0000000000000

x19 = 96.0000000000000

x20 = -64.0000000000000

x21 = 90.0000000000000

x22 = -40.0000000000000

x23 = -78.0000000000000

x24 = -90.0000000000000

x25 = -46.0000000000000

x26 = -96.0000000000000

x27 = -48.0000000000000

x28 = 68.0000000000000

x29 = -58.0000000000000

x30 = 48.0000000000000

x31 = -54.0000000000000

x32 = -34.0000000000000

x33 = 24.0000000000000

x34 = 26.0000000000000

x35 = 44.0000000000000

x36 = 38.0000000000000

x37 = -24.0000000000000

x38 = -88.0000000000000

x39 = 8.00000000000000

x40 = 18.0000000000000

x41 = -16.0000000000000

x42 = -42.0000000000000

x43 = -22.0000000000000

x44 = 62.0000000000000

x45 = -4.00000000000000

x46 = 42.0000000000000

x47 = 84.0000000000000

x48 = -84.0000000000000

x49 = -76.0000000000000

x50 = 72.0000000000000

x51 = 98.0000000000000

x52 = 74.0000000000000

x53 = 36.0000000000000

x54 = 30.0000000000000

x55 = -18.0000000000000

x56 = 14.0000000000000

x57 = 86.0000000000000

x58 = -94.0000000000000

x59 = 56.0000000000000

x60 = -70.0000000000000

x61 = -72.0000000000000

x62 = -5.55111512313000e-17

x63 = -52.0000000000000

x64 = 50.0000000000000

x65 = -28.0000000000000

x66 = -36.0000000000000

x67 = -30.0000000000000