cos(pi*x/3)=1

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

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

$$x_{1} = 0$$

x2 = 6

$$x_{2} = 6$$

x1 = -30.0000004278000

x2 = 66.0000000000000

x3 = 29.9999995722000

x4 = -54.0000004278000

x5 = 12.0000000000000

x6 = 78.0000000000000

x7 = -35.9999997919000

x8 = 90.0000000000000

x9 = 30.0000002081000

x10 = -101.999999792000

x11 = -48.0000000000000

x12 = 41.9999995722000

x13 = 83.9999995722000

x14 = 72.0000000000000

x15 = 78.0000002081000

x16 = -66.0000000000000

x17 = -5.99999979188000

x18 = 95.9999995722000

x19 = 96.0000002081000

x20 = 36.0000000000000

x21 = -59.9999997919000

x22 = 72.0000002081000

x23 = -54.0000000000000

x24 = -36.0000004278000

x25 = 2.08124927803000e-7

x26 = 90.0000002081000

x27 = -30.0000000000000

x28 = -12.0000000000000

x29 = 53.9999995722000

x30 = 6.00000020812000

x31 = -72.0000004278000

x32 = -11.9999997919000

x33 = -60.0000000000000

x34 = -23.9999997919000

x35 = 24.0000000000000

x36 = -24.0000004278000

x37 = 18.0000000000000

x38 = 23.9999995722000

x39 = -78.0000004278000

x40 = -83.9999997919000

x41 = 59.9999995722000

x42 = 24.0000002081000

x43 = -60.0000004278000

x44 = 0.0

x45 = -36.0000000000000

x46 = -78.0000000000000

x47 = 11.9999995722000

x48 = 35.9999995722000

x49 = 54.0000000000000

x50 = -71.9999997919000

x51 = 66.0000002081000

x52 = 60.0000000000000

x53 = 18.0000002081000

x54 = -4.27839045812000e-7

x55 = -77.9999997919000

x56 = 84.0000002081000

x57 = -96.0000004278000

x58 = -47.9999997919000

x59 = 48.0000000000000

x60 = -42.0000004278000

x61 = 60.0000002081000

x62 = -42.0000000000000

x63 = -48.0000004278000

x64 = -53.9999997919000

x65 = -84.0000000000000

x66 = -12.0000004278000

x67 = 54.0000002081000

x68 = -65.9999997919000

x69 = -66.0000004278000

x70 = -95.9999997919000

x71 = 30.0000000000000

x72 = 17.9999995722000

x73 = -6.00000000000000

x74 = 6.00000000000000

x75 = -84.0000004278000

x76 = -18.0000000000000

x77 = -90.0000000000000

x78 = 48.0000002081000

x79 = 77.9999995722000

x80 = 65.9999995722000

x81 = 12.0000002081000

x82 = -17.9999997919000

x83 = 101.999999572000

x84 = 42.0000002081000

x85 = -29.9999997919000

x86 = -96.0000000000000

x87 = 71.9999995722000

x88 = -6.00000042784000

x89 = 36.0000002081000

x90 = 89.9999995722000

x91 = -24.0000000000000

x92 = 5.99999957216000

x93 = 42.0000000000000

x94 = 84.0000000000000

x95 = 96.0000000000000

x96 = -89.9999997919000

x97 = -90.0000004278000

x98 = 47.9999995722000

x99 = -72.0000000000000

x100 = -18.0000004278000

x101 = -41.9999997919000