cos(pi*x/9)=1/2

$$cos{left (frac{pi x}{9} right )} = frac{1}{2}$$

Дано уравнение
$$cos{left (frac{pi x}{9} right )} = frac{1}{2}$$
– это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$frac{pi x}{9} = pi n + {acos}{left (frac{1}{2} right )}$$
$$frac{pi x}{9} = pi n – pi + {acos}{left (frac{1}{2} right )}$$
Или
$$frac{pi x}{9} = pi n + frac{pi}{3}$$
$$frac{pi x}{9} = pi n – frac{2 pi}{3}$$
, где n – любое целое число
Разделим обе части полученного ур-ния на
$$frac{pi}{9}$$
получим ответ:
$$x_{1} = frac{1}{pi} left(9 pi n + 3 piright)$$
$$x_{2} = frac{1}{pi} left(9 pi n – 6 piright)$$

$$x_{1} = 3$$

x2 = 15

$$x_{2} = 15$$

x1 = -7257.00000000000

x2 = -75.0000000000000

x3 = 111.000000000000

x4 = -87.0000000000000

x5 = 39.0000000000000

x6 = 3.00000000000000

x7 = -39.0000000000000

x8 = -93.0000000000000

x9 = -57.0000000000000

x10 = -7185.00000000000

x11 = -7329.00000000000

x12 = -7239.00000000000

x13 = -7203.00000000000

x14 = -15.0000000000000

x15 = -7365.00000000000

x16 = 57.0000000000000

x17 = -21.0000000000000

x18 = 87.0000000000000

x19 = 69.0000000000000

x20 = -7221.00000000000

x21 = 75.0000000000000

x22 = 123.000000000000

x23 = 93.0000000000000

x24 = 15.0000000000000

x25 = -3.00000000000000

x26 = -7275.00000000000

x27 = 51.0000000000000

x28 = 105.000000000000

x29 = -51.0000000000000

x30 = -69.0000000000000

x31 = -33.0000000000000

x32 = -7347.00000000000

x33 = -7293.00000000000

x34 = 33.0000000000000

x35 = -7167.00000000000

x36 = 21.0000000000000

x37 = -7311.00000000000