sin(3*x-pi/4)=-sqrt(3)/2

Дано

$$\sin{\left (3 x — \frac{\pi}{4} \right )} = \frac{-1 \sqrt{3}}{2}$$
Подробное решение
Дано уравнение
$$\sin{\left (3 x — \frac{\pi}{4} \right )} = \frac{-1 \sqrt{3}}{2}$$
— 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:
$$x_{1} = \frac{\pi n}{3} — \frac{\pi}{36}$$
$$x_{2} = \frac{\pi n}{3} — \frac{13 \pi}{36}$$

Ответ
Читайте также  x^3-6*x^2+11*x-6=0

-pi
x1 = —-
36

$$x_{1} = — \frac{\pi}{36}$$

19*pi
x2 = ——
36

$$x_{2} = \frac{19 \pi}{36}$$
Численный ответ

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

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