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3sin^2x-7sinx×cosx+2cos^2x=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
     2                             2       
3*sin (x) - 7*sin(x)*cos(x) + 2*cos (x) = 0
$$\left(3 \sin^{2}{\left(x \right)} - 7 \sin{\left(x \right)} \cos{\left(x \right)}\right) + 2 \cos^{2}{\left(x \right)} = 0$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
        /      ___\         /      ___\                                          
        |1   \/ 5 |         |1   \/ 5 |         /      ____\         /      ____\
- 2*atan|- - -----| - 2*atan|- + -----| - 2*atan\3 - \/ 10 / - 2*atan\3 + \/ 10 /
        \2     2  /         \2     2  /
$$- 2 \operatorname{atan}{\left(3 + \sqrt{10} \right)} + \left(\left(- 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} - 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)}\right) - 2 \operatorname{atan}{\left(3 - \sqrt{10} \right)}\right)$$ 
=
        /      ___\         /      ___\                                          
        |1   \/ 5 |         |1   \/ 5 |         /      ____\         /      ____\
- 2*atan|- + -----| - 2*atan|- - -----| - 2*atan\3 + \/ 10 / - 2*atan\3 - \/ 10 /
        \2     2  /         \2     2  /
$$- 2 \operatorname{atan}{\left(3 + \sqrt{10} \right)} - 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} - 2 \operatorname{atan}{\left(3 - \sqrt{10} \right)} - 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)}$$ 
producto
       /      ___\        /      ___\                                        
       |1   \/ 5 |        |1   \/ 5 |        /      ____\        /      ____\
-2*atan|- - -----|*-2*atan|- + -----|*-2*atan\3 - \/ 10 /*-2*atan\3 + \/ 10 /
       \2     2  /        \2     2  /
$$- 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)} \left(- 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}\right) \left(- 2 \operatorname{atan}{\left(3 - \sqrt{10} \right)}\right) \left(- 2 \operatorname{atan}{\left(3 + \sqrt{10} \right)}\right)$$ 
=
       /      ___\     /      ___\                                  
       |1   \/ 5 |     |1   \/ 5 |     /      ____\     /      ____\
16*atan|- + -----|*atan|- - -----|*atan\3 + \/ 10 /*atan\3 - \/ 10 /
       \2     2  /     \2     2  /
$$16 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)} \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} \operatorname{atan}{\left(3 - \sqrt{10} \right)} \operatorname{atan}{\left(3 + \sqrt{10} \right)}$$ 
16*atan(1/2 + sqrt(5)/2)*atan(1/2 - sqrt(5)/2)*atan(3 + sqrt(10))*atan(3 - sqrt(10))
Respuesta rápida [src] 
            /      ___\
            |1   \/ 5 |
x1 = -2*atan|- - -----|
            \2     2  /
$$x_{1} = - 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)}$$ 
            /      ___\
            |1   \/ 5 |
x2 = -2*atan|- + -----|
            \2     2  /
$$x_{2} = - 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}$$ 
            /      ____\
x3 = -2*atan\3 - \/ 10 /
$$x_{3} = - 2 \operatorname{atan}{\left(3 - \sqrt{10} \right)}$$ 
            /      ____\
x4 = -2*atan\3 + \/ 10 /
$$x_{4} = - 2 \operatorname{atan}{\left(3 + \sqrt{10} \right)}$$ 
x4 = -2*atan(3 + sqrt(10))
Respuesta numérica [src] 
x1 = 60.0120109726027
x2 = -96.2822235434895
x3 = -17.7424072037447
x4 = -43.6605465958605
x5 = 70.2221870967695
x6 = 0.321750554396642
x7 = -100.209214360477
x8 = 13.6735193321533
x9 = 100.85271546927
x10 = -74.2910749683609
x11 = -39.7335557788732
x12 = 35.6646679072818
x13 = -56.2269172102196
x14 = -1146.35956800588
x15 = -53.0853245566298
x16 = -37.3773612886809
x17 = 38.0208623974742
x18 = 95.3549283254879
x19 = -93.9260290532972
x20 = 8973.49576737024
x21 = 4.24874137138388
x22 = -36.5919631252834
x23 = -8.31762924297529
x24 = 88.2863448549109
x25 = -14.6008145501549
x26 = 66.2951962797823
x27 = -42.875148432463
x28 = 44.3040477046537
x29 = -34.2357686350911
x30 = 28.5960844367048
x31 = -87.6428437461176
x32 = 56.8704183190129
x33 = 79.6469650575389
x34 = 48.231038521641
x35 = -58.583111700412
x36 = 34.8792697438844
x37 = -1294649.22539564
x38 = 41.9478532144614
x39 = 72.5783815869619
x40 = -30.3087778181038
x41 = 78.8615668941415
x42 = -80.5742602755405
x43 = -83.7158529291303
x44 = -15.3862127135523
x45 = -52.2999263932324
x46 = 16.0297138223456
x47 = 94.5695301620904
x48 = 26.2398899465124
x49 = 29.3814826001022
x50 = 82.0031595477313
x51 = -89.9990382363099
x52 = -27.9525833279115
x53 = -97.067621706887
x54 = -81.359658438938
x55 = -75.0764731317584
x56 = -78.2180657853482
x57 = -5.96143475278294
x58 = -46.0167410860528
x59 = 73.3637797503593
x60 = 57.6558164824104
x61 = -31.0941759815013
x62 = -9.10302740637274
x63 = 92.2133356718981
x64 = -65.651695170989
x65 = 51.3726311752308
x66 = -71.9348804781686
x67 = 4627.88772929216
x68 = 19.9567046393328
x69 = -68.0078896611814
x70 = 22.3128991295252
x71 = 85.9301503647185
x72 = 50.5872330118333
x73 = 63.93900178959
x74 = 9.74652851516602
x75 = -59.3685098638094
x76 = -49.9437319030401
x77 = -2.0344439357957
x78 = -24.0255925109243
x79 = 12.8881211687558
x80 = -61.7247043540018
x81 = 6.60493586157623
x82 = 7.39033402497368
x83 = -21.6693980207319
x83 = -21.6693980207319
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