sin(pi*x/3)=1/2

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

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

$$x_{1} = frac{1}{2}$$

x2 = 5/2

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

x1 = -23.5000000000000

x2 = -87.5000000000000

x3 = -77.5000000000000

x4 = -21.5000000000000

x5 = 42.5000000000000

x6 = 14.5000000000000

x7 = 92.5000000000000

x8 = -95.5000000000000

x9 = -35.5000000000000

x10 = 56.5000000000000

x11 = -11.5000000000000

x12 = 48.5000000000000

x13 = 12.5000000000000

x14 = -101.500000000000

x15 = -71.5000000000000

x16 = 80.5000000000000

x17 = 24.5000000000000

x18 = 54.5000000000000

x19 = -29.5000000000000

x20 = 38.5000000000000

x21 = -99.5000000000000

x22 = 50.5000000000000

x23 = 32.5000000000000

x24 = 86.5000000000000

x25 = -81.5000000000000

x26 = -59.5000000000000

x27 = 0.500000000000000

x28 = 66.5000000000000

x29 = 68.5000000000000

x30 = 98.5000000000000

x31 = -15.5000000000000

x32 = 72.5000000000000

x33 = 84.5000000000000

x34 = -5.50000000000000

x35 = 90.5000000000000

x36 = -93.5000000000000

x37 = -89.5000000000000

x38 = 74.5000000000000

x39 = 60.5000000000000

x40 = -45.5000000000000

x41 = 26.5000000000000

x42 = -63.5000000000000

x43 = 78.5000000000000

x44 = -83.5000000000000

x45 = 6.50000000000000

x46 = -33.5000000000000

x47 = -53.5000000000000

x48 = -51.5000000000000

x49 = 36.5000000000000

x50 = -3.50000000000000

x51 = 44.5000000000000

x52 = -27.5000000000000

x53 = -39.5000000000000

x54 = 18.5000000000000

x55 = -69.5000000000000

x56 = -65.5000000000000

x57 = 20.5000000000000

x58 = 96.5000000000000

x59 = 30.5000000000000

x60 = -47.5000000000000

x61 = -9.50000000000000

x62 = -41.5000000000000

x63 = -75.5000000000000

x64 = 2.50000000000000

x65 = 62.5000000000000

x66 = -17.5000000000000

x67 = -57.5000000000000

x68 = 8.50000000000000