sin(3*x)=1

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

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

pi
x1 = —
6

$$x_{1} = frac{pi}{6}$$

x1 = 48.6946859684000

x2 = 6.80678394974000

x3 = 80.1106131529000

x4 = 21.4675499465000

x5 = -85.3466004035000

x6 = -89.5353907408000

x7 = -41.3643034313000

x8 = -14.1371668430000

x9 = 84.2994028383000

x10 = -91.6297858015000

x11 = 19.3731547553000

x12 = 17.2787592808000

x13 = 52.8834762893000

x14 = -51.8362786905000

x15 = -16.2315619073000

x16 = -7.85398150192000

x17 = 54.9778717979000

x18 = 94.7713782337000

x19 = 46.6002908749000

x20 = -1.57079642588000

x21 = -28.7979326033000

x22 = -85.3466005834000

x23 = -3.66519148255000

x24 = 69.6386373203000

x25 = -100.007366131000

x26 = 42.4115007321000

x27 = 90.5825880288000

x28 = -81.1578103225000

x29 = -22.5147471968000

x30 = -83.2522054763000

x31 = -12.0427717978000

x32 = 40.3171056776000

x33 = -43.4586985139000

x34 = 73.8274274735000

x35 = 4.71238881902000

x36 = -49.7418836877000

x37 = -60.2138590636000

x38 = -24.6091423681000

x39 = -45.5530935835000

x40 = -64.4026492298000

x41 = 71.7330324040000

x42 = 25.6563401677000

x43 = 50.7890810906000

x44 = -68.5914394977000

x45 = -47.6474886423000

x46 = -56.0250689630000

x47 = -62.3082541392000

x48 = -18.3259569855000

x49 = 31.9395253655000

x50 = 29.8451303155000

x51 = 75.9218225274000

x52 = 10.9955746929000

x53 = 38.2227106406000

x54 = 63.3554518703000

x55 = 96.8657734100000

x56 = -3.66519119284000

x57 = -26.7035377567000

x58 = -87.4409956690000

x59 = -53.9306741018000

x60 = -35.0811179202000

x61 = 65.4498470877000

x62 = 61.2610563292000

x63 = 88.4881929539000

x64 = -58.1194640022000

x65 = -39.2699083293000

x66 = 86.3937978905000

x67 = 23.5619450702000

x68 = 34.0339203588000

x69 = 67.5442422190000

x70 = 92.6769831187000

x71 = 2.61799372150000

x72 = -37.1755131460000

x73 = -5.75958652427000

x74 = -20.4203520794000

x75 = -37.1755131882000

x76 = 0.523598641616000

x77 = -9.94837684429000

x78 = 98.9601688300000

x79 = 78.0162175421000

x80 = 82.2050078076000

x81 = 44.5058957976000

x82 = -70.6858348165000

x83 = -95.8185758683000

x84 = -66.4970445282000

x85 = -66.4970443417000

x86 = 27.7507352486000

x87 = -79.0634150012000

x88 = -93.7241808502000

x89 = 8.90117917814000