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4*cos(x)^(2)+(5/2)*sin(2*x)-3*sin(x)^(2)=3 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
     2      5*sin(2*x)        2       
4*cos (x) + ---------- - 3*sin (x) = 3
                2
$$\left(\frac{5 \sin{\left(2 x \right)}}{2} + 4 \cos^{2}{\left(x \right)}\right) - 3 \sin^{2}{\left(x \right)} = 3$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
     pi
x1 = --
     4
$$x_{1} = \frac{\pi}{4}$$ 
                        /log(37)      /  ____\\
x2 = pi - atan(1/6) + I*|------- - log\\/ 37 /|
                        \   2                 /
$$x_{2} = - \operatorname{atan}{\left(\frac{1}{6} \right)} + \pi + i \left(- \log{\left(\sqrt{37} \right)} + \frac{\log{\left(37 \right)}}{2}\right)$$ 
                    /log(37)      /  ____\\
x3 = -atan(1/6) + I*|------- - log\\/ 37 /|
                    \   2                 /
$$x_{3} = - \operatorname{atan}{\left(\frac{1}{6} \right)} + i \left(- \log{\left(\sqrt{37} \right)} + \frac{\log{\left(37 \right)}}{2}\right)$$ 
           /   ___\
x4 = -I*log\-\/ I /
$$x_{4} = - i \log{\left(- \sqrt{i} \right)}$$ 
x4 = -i*log(-sqrt(i))
Suma y producto de raíces [src] 
suma
pi                      /log(37)      /  ____\\                  /log(37)      /  ____\\        /   ___\
-- + pi - atan(1/6) + I*|------- - log\\/ 37 /| + -atan(1/6) + I*|------- - log\\/ 37 /| - I*log\-\/ I /
4                       \   2                 /                  \   2                 /
$$- i \log{\left(- \sqrt{i} \right)} + \left(\left(\frac{\pi}{4} + \left(- \operatorname{atan}{\left(\frac{1}{6} \right)} + \pi + i \left(- \log{\left(\sqrt{37} \right)} + \frac{\log{\left(37 \right)}}{2}\right)\right)\right) + \left(- \operatorname{atan}{\left(\frac{1}{6} \right)} + i \left(- \log{\left(\sqrt{37} \right)} + \frac{\log{\left(37 \right)}}{2}\right)\right)\right)$$ 
=
               5*pi        /   ___\       /log(37)      /  ____\\
-2*atan(1/6) + ---- - I*log\-\/ I / + 2*I*|------- - log\\/ 37 /|
                4                         \   2                 /
$$- i \log{\left(- \sqrt{i} \right)} - 2 \operatorname{atan}{\left(\frac{1}{6} \right)} + \frac{5 \pi}{4} + 2 i \left(- \log{\left(\sqrt{37} \right)} + \frac{\log{\left(37 \right)}}{2}\right)$$ 
producto
pi /                   /log(37)      /  ____\\\ /               /log(37)      /  ____\\\ /      /   ___\\
--*|pi - atan(1/6) + I*|------- - log\\/ 37 /||*|-atan(1/6) + I*|------- - log\\/ 37 /||*\-I*log\-\/ I //
4  \                   \   2                 // \               \   2                 //
$$- i \log{\left(- \sqrt{i} \right)} \frac{\pi}{4} \left(- \operatorname{atan}{\left(\frac{1}{6} \right)} + \pi + i \left(- \log{\left(\sqrt{37} \right)} + \frac{\log{\left(37 \right)}}{2}\right)\right) \left(- \operatorname{atan}{\left(\frac{1}{6} \right)} + i \left(- \log{\left(\sqrt{37} \right)} + \frac{\log{\left(37 \right)}}{2}\right)\right)$$ 
=
                                   /   ___\
pi*I*(pi - atan(1/6))*atan(1/6)*log\-\/ I /
-------------------------------------------
                     4
$$\frac{i \pi \left(\pi - \operatorname{atan}{\left(\frac{1}{6} \right)}\right) \log{\left(- \sqrt{i} \right)} \operatorname{atan}{\left(\frac{1}{6} \right)}}{4}$$ 
pi*i*(pi - atan(1/6))*atan(1/6)*log(-sqrt(i))/4
Respuesta numérica [src] 
x1 = 94.0826309302792
x2 = 32.2013246992954
x3 = -27.4889357189107
x4 = 10.2101761241668
x5 = -21.2057504117311
x6 = -66.1385944028003
x7 = 79.3252145031423
x8 = -52.621676947629
x9 = 82.4668071567321
x10 = -81.8465576707492
x11 = 40.6755558192527
x12 = -77.7544181763474
x13 = -14.9225651045515
x14 = -179.235929932033
x15 = 16.4933614313464
x16 = 41.6261026600648
x17 = -84.988150324339
x18 = -74.6128255227576
x19 = -46.3384916404494
x20 = -5.49778714378214
x21 = -84.037603483527
x22 = 91.8915851175014
x23 = -30.6305283725005
x24 = -55.7632696012188
x25 = -71.4712328691678
x26 = 56.3835190872016
x27 = -88.1297429779288
x28 = 60.4756585816035
x29 = 72.0914823551506
x30 = 3.92699081698724
x31 = -47.2890384812615
x32 = 78.3746676623302
x33 = -31.5810752133126
x34 = 50.1003337800221
x35 = 38.484510006475
x36 = 65.808297047971
x37 = 3543.55136457187
x38 = -90.3207887907066
x39 = -97.5545209386982
x40 = 98.174770424681
x41 = -25.297889906133
x42 = 43.8171484728425
x43 = -18.0641577581413
x44 = 76.1836218495525
x45 = -75.5633723635697
x46 = -9.58992663818401
x47 = -40.0553063332699
x48 = 34.3923705120731
x49 = -22.1562972525432
x50 = -68.329640215578
x51 = 35.3429173528852
x52 = -59.8554090956207
x53 = -936.359759447173
x54 = 28.1091852048935
x55 = -33.7721210260903
x56 = 62.6667043943812
x57 = -96.6039740978861
x58 = -49.4800842940392
x59 = 18.6844072441241
x60 = -3.30674133100442
x61 = 25.9181393921158
x62 = 85.6083998103219
x63 = 12.4012219369445
x64 = -99.7455667514759
x65 = -37.8642605204921
x66 = 68.9498897015608
x67 = 13.3517687777566
x68 = 84.6578529695098
x69 = -8.63937979737193
x70 = 54.1924732744239
x71 = -24.3473430653209
x72 = -0.165148677414627
x73 = 63.6172512351933
x74 = 19.6349540849362
x75 = 90.9410382766894
x76 = -93.4623814442964
x77 = -15.8731119453636
x78 = 6.11803662976496
x79 = 21.8259998977139
x80 = -44.1474458276717
x81 = 87.7994456230996
x82 = -11.7809724509617
x83 = -62.0464549083984
x84 = 69.9004365423729
x85 = 57.3340659280137
x86 = -91.2713356315186
x87 = -53.5722237884411
x88 = -2.35619449019234
x89 = -1196.16140285431
x90 = 47.9092879672443
x91 = -69.2801870563901
x92 = 100.365816237459
x92 = 100.365816237459
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