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

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

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

$$x_{1} = 2$$

x2 = 4

$$x_{2} = 4$$

x1 = -32.0000000000000

x2 = 542.000000000000

x3 = 94.0000000000000

x4 = 52.0000000000000

x5 = 520.000000000000

x6 = 32.0000000000000

x7 = 92.0000000000000

x8 = -100.000000000000

x9 = 556.000000000000

x10 = 1546.00000000000

x11 = 16.0000000000000

x12 = -46.0000000000000

x13 = -50.0000000000000

x14 = -88.0000000000000

x15 = 80.0000000000000

x16 = 760.000000000000

x17 = 4.00000000000000

x18 = 34.0000000000000

x19 = 2.00000000000000

x20 = 70.0000000000000

x21 = -82.0000000000000

x22 = 584.000000000000

x23 = -58.0000000000000

x24 = -28.0000000000000

x25 = -10.0000000000000

x26 = -64.0000000000000

x27 = 206.000000000000

x28 = -40.0000000000000

x29 = -14.0000000000000

x30 = -92.0000000000000

x31 = -56.0000000000000

x32 = 616.000000000000

x33 = 40.0000000000000

x34 = -8.00000000000000

x35 = 46.0000000000000

x36 = 532.000000000000

x37 = 22.0000000000000

x38 = 58.0000000000000

x39 = 26.0000000000000

x40 = 76.0000000000000

x41 = 28.0000000000000

x42 = 74.0000000000000

x43 = 650.000000000000

x44 = 8.00000000000000

x45 = -52.0000000000000

x46 = -38.0000000000000

x47 = 100.000000000000

x48 = -44.0000000000000

x49 = -68.0000000000000

x50 = -4.00000000000000

x51 = 62.0000000000000

x52 = 640.000000000000

x53 = 578.000000000000

x54 = 82.0000000000000

x55 = -86.0000000000000

x56 = -76.0000000000000

x57 = -22.0000000000000

x58 = -34.0000000000000

x59 = 98.0000000000000

x60 = -62.0000000000000

x61 = 38.0000000000000

x62 = 50.0000000000000

x63 = 20.0000000000000

x64 = 64.0000000000000

x65 = 56.0000000000000

x66 = 68.0000000000000

x67 = 14.0000000000000

x68 = -26.0000000000000

x69 = -2.00000000000000

x70 = 88.0000000000000

x71 = 10.0000000000000

x72 = 86.0000000000000

x73 = -94.0000000000000

x74 = -20.0000000000000

x75 = -70.0000000000000

x76 = -98.0000000000000

x77 = 44.0000000000000

x78 = -74.0000000000000

x79 = -16.0000000000000

x80 = -80.0000000000000