cos(2*x+pi/2)=sqrt(2)*sin(x)

Решение любых уравнений, Решение уравнений Работа проверена: margo200 Время решения: 15 мин Сложность: 3.8

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Дано

$$cos{left (2 x + frac{pi}{2} right )} = sqrt{2} sin{left (x right )}$$

Ответ

$$x_{1} = 0$$

x2 = pi

$$x_{2} = pi$$

3*pi /log(2) / ___
x3 = – —- + I*|—— – log/ 2 /|
4 2 /

$$x_{3} = – frac{3 pi}{4} + i left(- log{left (sqrt{2} right )} + frac{1}{2} log{left (2 right )}right)$$

3*pi /log(2) / ___
x4 = —- + I*|—— – log/ 2 /|
4 2 /

$$x_{4} = frac{3 pi}{4} + i left(- log{left (sqrt{2} right )} + frac{1}{2} log{left (2 right )}right)$$

Численный ответ

x1 = -77.7544181763000

x2 = 21.2057504117000

x3 = 90.3207887907000

x4 = -12.5663706144000

x5 = 77.7544181763000

x6 = -71.4712328692000

x7 = -47.9092879672000

x8 = 56.5486677646000

x9 = 75.3982236862000

x10 = 18.8495559215000

x11 = 58.9048622548000

x12 = 12.5663706144000

x13 = 84.0376034835000

x14 = 54.1924732744000

x15 = 2.35619449019000

x16 = 43.9822971503000

x17 = 94.2477796077000

x18 = -33.7721210261000

x19 = 10.2101761242000

x20 = -87.9645943005000

x21 = -73.0420291960000

x22 = 115.453530019000

x23 = 599.258798672000

x24 = 62.8318530718000

x25 = -2.35619449019000

x26 = 87.9645943005000

x27 = 28.2743338823000

x28 = -54.1924732744000

x29 = 35.3429173529000

x30 = -46.3384916404000

x31 = 40.0553063333000

x32 = -96.6039740979000

x33 = 41.6261026601000

x34 = -79.3252145031000

x35 = -81.6814089933000

x36 = -21.9911485751000

x37 = -37.6991118431000

x38 = 31.4159265359000

x39 = 46.3384916404000

x40 = 21.9911485751000

x41 = -100.530964915000

x42 = 0.0

x43 = 399.767665169000

x44 = -94.2477796077000

x45 = 14.9225651046000

x46 = 85.6083998103000

x47 = -191.637151869000

x48 = 50.2654824574000

x49 = -59.6902604182000

x50 = 29.0597320457000

x51 = -25.1327412287000

x52 = -43.9822971503000

x53 = -90.3207887907000

x54 = 71.4712328692000

x55 = 3.92699081699000

x56 = 72.2566310326000

x57 = -6.28318530718000

x58 = 1523.67243699000

x59 = -65.9734457254000

x60 = 65.1880475620000

x61 = 98.1747704247000

x62 = -56.5486677646000

x63 = 65.9734457254000

x64 = -58.9048622548000

x65 = -84.0376034835000

x66 = -3801.32711084000

x67 = -35.3429173529000

x68 = -41.6261026601000

x69 = -14.9225651046000

x70 = -29.0597320457000

x71 = -91.8915851175000

x72 = -15.7079632679000

x73 = 81.6814089933000

x74 = 96.6039740979000

x75 = 3.14159265359000

x76 = 100.530964915000

x77 = -27.4889357189000

x78 = -342.433599241000

x79 = -8.63937979737000

x80 = -31.4159265359000

x81 = -40.0553063333000

x82 = -85.6083998103000

x83 = -75.3982236862000

x84 = -69.1150383790000

x85 = 79.3252145031000

x86 = -9.42477796077000

x87 = 6.28318530718000

x88 = -98.1747704247000

x89 = 47.9092879672000

x90 = 16.4933614313000

x91 = -3.92699081699000

x92 = -50.2654824574000

x93 = 52.6216769476000

x94 = -52.6216769476000

x95 = 91.8915851175000

x96 = 37.6991118431000

x97 = 8.63937979737000

4.13

margo200

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cos(2x+pi/2)=sqrt(2)sin(x)

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