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
$$3 x = 2 pi n – frac{pi}{2}$$
$$3 x = 2 pi n + frac{3 pi}{2}$$
, где n – любое целое число
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = frac{2 pi}{3} n – frac{pi}{6}$$
$$x_{2} = frac{2 pi}{3} n + frac{pi}{2}$$

-pi
x1 = —-
6

$$x_{1} = – frac{pi}{6}$$

pi
x2 = —
2

$$x_{2} = frac{pi}{2}$$

x1 = 68.5914394518000

x2 = 20.4203521531000

x3 = 14.1371670950000

x4 = 47.6474887441000

x5 = 72.7802296619000

x6 = -78.0162175465000

x7 = -65.4498470915000

x8 = 41.3643033140000

x9 = 70.6858345434000

x10 = -0.523598624935000

x11 = 5.75958667072000

x12 = 3.66519159119000

x13 = 539.830337691000

x14 = -63.3554520074000

x15 = 32.9867232717000

x16 = 12.0427717609000

x17 = -29.8451300979000

x18 = -69.6386372219000

x19 = -15.1843646196000

x20 = 16.2315620580000

x21 = -59.1666617558000

x22 = -40.3171055622000

x23 = 26.7035373936000

x24 = 85.3466004238000

x25 = -96.8657738809000

x26 = -84.2994027162000

x27 = 64.4026493113000

x28 = -6.80678413492000

x29 = 97.9129711080000

x30 = 7.85398173633000

x31 = 39.2699077976000

x32 = 93.7241809815000

x33 = 1.57079649552000

x34 = -10.9955742377000

x35 = -23.5619450047000

x36 = -46.6002909322000

x37 = 18.3259570975000

x38 = -21.4675499362000

x39 = -36.1283154225000

x40 = 89.5353907930000

x41 = -71.7330322691000

x42 = -90.5825880643000

x43 = 51.8362788946000

x44 = 53.9306739466000

x45 = 74.8746248486000

x46 = -80.1106125820000

x47 = -73.8274272804000

x48 = -48.6946862836000

x49 = 43.4586985173000

x50 = -19.3731548550000

x51 = -67.5442421622000

x52 = -17.2787597553000

x53 = 62.3082542579000

x54 = -13.0899693729000

x55 = -2.61799380552000

x56 = -61.2610569030000

x57 = 83.2522049225000

x58 = -88.4881929146000

x59 = 100.007366130000

x60 = 56.0250689520000

x61 = -31.9395254619000

x62 = -25.6563400625000

x63 = 9.94837678402000

x64 = -86.3937978053000

x65 = -82.2050076419000

x66 = -57.0722664632000

x67 = -34.0339203801000

x68 = -27.7507351062000

x69 = 60.2138592238000

x70 = 95.8185760523000

x71 = -44.5058957690000

x72 = -4.71238923573000

x73 = -75.9218227440000

x74 = 87.4409956574000

x75 = -92.6769833550000

x76 = 76.9690203133000

x77 = 28.7979325198000

x78 = -42.4115006545000

x79 = 45.5530936447000

x80 = 22.5147472195000

x81 = 49.7418838263000

x82 = 24.6091422981000

x83 = 66.4970443757000

x84 = 30.8923277324000

x85 = -38.2227104854000

x86 = 91.6297858964000

x87 = -42.4115010822000