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Реши любую задачу с помощью нейросети.
$$sin{left (3 x – frac{pi}{4} right )} = frac{-1 sqrt{3}}{2}$$
– это простейшее тригонометрическое ур-ние
Разделим обе части ур-ния на -1
Ур-ние превратится в
$$cos{left (3 x + frac{pi}{4} right )} = frac{sqrt{3}}{2}$$
Это ур-ние преобразуется в
$$3 x + frac{pi}{4} = pi n + {acos}{left (frac{sqrt{3}}{2} right )}$$
$$3 x + frac{pi}{4} = pi n – pi + {acos}{left (frac{sqrt{3}}{2} right )}$$
Или
$$3 x + frac{pi}{4} = pi n + frac{pi}{6}$$
$$3 x + frac{pi}{4} = pi n – frac{5 pi}{6}$$
, где n – любое целое число
Перенесём
$$frac{pi}{4}$$
в правую часть ур-ния
с противоположным знаком, итого:
$$3 x = pi n – frac{pi}{12}$$
$$3 x = pi n – frac{13 pi}{12}$$
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = frac{pi n}{3} – frac{pi}{36}$$
$$x_{2} = frac{pi n}{3} – frac{13 pi}{36}$$
-pi
x1 = —-
36
19*pi
x2 = —–
36
x1 = 52.2726110972000
x2 = -10.9083078250000
x3 = -39.8807734081000
x4 = 75.3109572236000
x5 = 64.4899158612000
x6 = -96.4294411727000
x7 = 87.8773278379000
x8 = -75.8345559992000
x9 = -54.8906049752000
x10 = -48.2583538176000
x11 = 37.6118453805000
x12 = 39.7062404829000
x13 = -0.0872664625997000
x14 = 62.3955207588000
x15 = -16.8424272817000
x16 = 48.0838208924000
x17 = 20.5076187109000
x18 = -69.5513706920000
x19 = -67.4569755896000
x20 = 41.4515697349000
x21 = -83.8630705583000
x22 = -98.8729021255000
x23 = 50.1782159948000
x24 = 68.6787060660000
x25 = 98.0002374995000
x26 = 12.1300383014000
x27 = -6.37045176978000
x28 = 92.0661180427000
x29 = 25.0454747661000
x30 = 66.5843109636000
x31 = 45.9894257901000
x32 = -94.3350460703000
x33 = 41.8006355853000
x34 = 71.1221670188000
x35 = 14.2244334038000
x36 = -63.2681853848000
x37 = -4647.54999867000
x38 = -29.7578637465000
x39 = -46.1639587153000
x40 = -408402.943443000
x41 = 85.7829327355000
x42 = -44.0695636129000
x43 = -8.46484687217000
x44 = 81.5941425307000
x45 = -90.1462558655000
x46 = 27.1398698685000
x47 = 16.3188285061000
x48 = 56.1123354516000
x49 = -65.3625804872000
x50 = -31.8522588489000
x51 = -21.3802833369000
x52 = -4.27605666739000
x53 = -19.2858882345000
x54 = -80.0233462039000
x55 = -37.7863783057000
x56 = -60.8247244320000
x57 = -23.4746784393000
x58 = 10.0356431990000
x59 = -50.3527489200000
x60 = -108.995811787000
x61 = -41.9751685105000
x62 = 100.094632602000
x63 = 18.4132236085000
x64 = -27.6634686441000
x65 = 33.0739893253000
x66 = 43.8950306877000
x67 = -81.7686754559000
x68 = -25.5690735417000
x69 = -73.7401608968000
x70 = -33.9466539513000
x71 = 60.3011256564000
x72 = -92.2406509679000
x73 = -85.9574656607000
x74 = 4.10152374219000
x75 = 94.1605131451000
x76 = 2.00712863979000
x77 = 96.2549082475000
x78 = -50.7018147704000
x79 = 89.9717229403000
x80 = 77.0562864755000
x81 = 58.2067305540000
x82 = 8.29031394697000
x83 = -71.6457657944000
x84 = 35.5174502781000
x85 = -77.9289511015000
x86 = 22.6020138133000
x87 = 54.0179403492000
x88 = 6.19591884458000
x89 = 269.740635896000
x90 = 24.6964089157000
x91 = 79.4997474283000
x92 = -35.6919832033000
x93 = -52.4471440224000
x94 = 83.6885376331000
x95 = -2.18166156499000
x96 = -88.0518607631000
