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6sin^2x+3cosxsinx-2cos^2x=3 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
     2                             2       
6*sin (x) + 3*cos(x)*sin(x) - 2*cos (x) = 3
$$\left(6 \sin^{2}{\left(x \right)} + \sin{\left(x \right)} 3 \cos{\left(x \right)}\right) - 2 \cos^{2}{\left(x \right)} = 3$$
Gráfica
Respuesta rápida [src]
           /                         _______________\
           |         ____     ___   /          ____ |
           |  3    \/ 69    \/ 2 *\/  89 - 3*\/ 69  |
x1 = 2*atan|- -- + ------ + ------------------------|
           \  10     10                10           /
$$x_{1} = 2 \operatorname{atan}{\left(- \frac{3}{10} + \frac{\sqrt{69}}{10} + \frac{\sqrt{2} \sqrt{89 - 3 \sqrt{69}}}{10} \right)}$$
            /                       _______________\
            |       ____     ___   /          ____ |
            |3    \/ 69    \/ 2 *\/  89 + 3*\/ 69  |
x2 = -2*atan|-- + ------ + ------------------------|
            \10     10                10           /
$$x_{2} = - 2 \operatorname{atan}{\left(\frac{3}{10} + \frac{\sqrt{69}}{10} + \frac{\sqrt{2} \sqrt{3 \sqrt{69} + 89}}{10} \right)}$$
            /                       _______________\
            |       ____     ___   /          ____ |
            |3    \/ 69    \/ 2 *\/  89 - 3*\/ 69  |
x3 = -2*atan|-- - ------ + ------------------------|
            \10     10                10           /
$$x_{3} = - 2 \operatorname{atan}{\left(- \frac{\sqrt{69}}{10} + \frac{3}{10} + \frac{\sqrt{2} \sqrt{89 - 3 \sqrt{69}}}{10} \right)}$$
            /                       _______________\
            |       ____     ___   /          ____ |
            |3    \/ 69    \/ 2 *\/  89 + 3*\/ 69  |
x4 = -2*atan|-- + ------ - ------------------------|
            \10     10                10           /
$$x_{4} = - 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 \sqrt{69} + 89}}{10} + \frac{3}{10} + \frac{\sqrt{69}}{10} \right)}$$
x4 = -2*atan(-sqrt(2)*sqrt(3*sqrt(69) + 89)/10 + 3/10 + sqrt(69)/10)
Suma y producto de raíces [src]
suma
      /                         _______________\         /                       _______________\         /                       _______________\         /                       _______________\
      |         ____     ___   /          ____ |         |       ____     ___   /          ____ |         |       ____     ___   /          ____ |         |       ____     ___   /          ____ |
      |  3    \/ 69    \/ 2 *\/  89 - 3*\/ 69  |         |3    \/ 69    \/ 2 *\/  89 + 3*\/ 69  |         |3    \/ 69    \/ 2 *\/  89 - 3*\/ 69  |         |3    \/ 69    \/ 2 *\/  89 + 3*\/ 69  |
2*atan|- -- + ------ + ------------------------| - 2*atan|-- + ------ + ------------------------| - 2*atan|-- - ------ + ------------------------| - 2*atan|-- + ------ - ------------------------|
      \  10     10                10           /         \10     10                10           /         \10     10                10           /         \10     10                10           /
$$\left(- 2 \operatorname{atan}{\left(- \frac{\sqrt{69}}{10} + \frac{3}{10} + \frac{\sqrt{2} \sqrt{89 - 3 \sqrt{69}}}{10} \right)} + \left(- 2 \operatorname{atan}{\left(\frac{3}{10} + \frac{\sqrt{69}}{10} + \frac{\sqrt{2} \sqrt{3 \sqrt{69} + 89}}{10} \right)} + 2 \operatorname{atan}{\left(- \frac{3}{10} + \frac{\sqrt{69}}{10} + \frac{\sqrt{2} \sqrt{89 - 3 \sqrt{69}}}{10} \right)}\right)\right) - 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 \sqrt{69} + 89}}{10} + \frac{3}{10} + \frac{\sqrt{69}}{10} \right)}$$
=
        /                       _______________\         /                       _______________\         /                       _______________\         /                         _______________\
        |       ____     ___   /          ____ |         |       ____     ___   /          ____ |         |       ____     ___   /          ____ |         |         ____     ___   /          ____ |
        |3    \/ 69    \/ 2 *\/  89 - 3*\/ 69  |         |3    \/ 69    \/ 2 *\/  89 + 3*\/ 69  |         |3    \/ 69    \/ 2 *\/  89 + 3*\/ 69  |         |  3    \/ 69    \/ 2 *\/  89 - 3*\/ 69  |
- 2*atan|-- - ------ + ------------------------| - 2*atan|-- + ------ - ------------------------| - 2*atan|-- + ------ + ------------------------| + 2*atan|- -- + ------ + ------------------------|
        \10     10                10           /         \10     10                10           /         \10     10                10           /         \  10     10                10           /
$$- 2 \operatorname{atan}{\left(\frac{3}{10} + \frac{\sqrt{69}}{10} + \frac{\sqrt{2} \sqrt{3 \sqrt{69} + 89}}{10} \right)} - 2 \operatorname{atan}{\left(- \frac{\sqrt{69}}{10} + \frac{3}{10} + \frac{\sqrt{2} \sqrt{89 - 3 \sqrt{69}}}{10} \right)} - 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 \sqrt{69} + 89}}{10} + \frac{3}{10} + \frac{\sqrt{69}}{10} \right)} + 2 \operatorname{atan}{\left(- \frac{3}{10} + \frac{\sqrt{69}}{10} + \frac{\sqrt{2} \sqrt{89 - 3 \sqrt{69}}}{10} \right)}$$
producto
      /                         _______________\        /                       _______________\        /                       _______________\        /                       _______________\
      |         ____     ___   /          ____ |        |       ____     ___   /          ____ |        |       ____     ___   /          ____ |        |       ____     ___   /          ____ |
      |  3    \/ 69    \/ 2 *\/  89 - 3*\/ 69  |        |3    \/ 69    \/ 2 *\/  89 + 3*\/ 69  |        |3    \/ 69    \/ 2 *\/  89 - 3*\/ 69  |        |3    \/ 69    \/ 2 *\/  89 + 3*\/ 69  |
2*atan|- -- + ------ + ------------------------|*-2*atan|-- + ------ + ------------------------|*-2*atan|-- - ------ + ------------------------|*-2*atan|-- + ------ - ------------------------|
      \  10     10                10           /        \10     10                10           /        \10     10                10           /        \10     10                10           /
$$2 \operatorname{atan}{\left(- \frac{3}{10} + \frac{\sqrt{69}}{10} + \frac{\sqrt{2} \sqrt{89 - 3 \sqrt{69}}}{10} \right)} \left(- 2 \operatorname{atan}{\left(\frac{3}{10} + \frac{\sqrt{69}}{10} + \frac{\sqrt{2} \sqrt{3 \sqrt{69} + 89}}{10} \right)}\right) \left(- 2 \operatorname{atan}{\left(- \frac{\sqrt{69}}{10} + \frac{3}{10} + \frac{\sqrt{2} \sqrt{89 - 3 \sqrt{69}}}{10} \right)}\right) \left(- 2 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 \sqrt{69} + 89}}{10} + \frac{3}{10} + \frac{\sqrt{69}}{10} \right)}\right)$$
=
        /                         _______________\     /                       _______________\     /                       _______________\     /                       _______________\
        |         ____     ___   /          ____ |     |       ____     ___   /          ____ |     |       ____     ___   /          ____ |     |       ____     ___   /          ____ |
        |  3    \/ 69    \/ 2 *\/  89 - 3*\/ 69  |     |3    \/ 69    \/ 2 *\/  89 - 3*\/ 69  |     |3    \/ 69    \/ 2 *\/  89 + 3*\/ 69  |     |3    \/ 69    \/ 2 *\/  89 + 3*\/ 69  |
-16*atan|- -- + ------ + ------------------------|*atan|-- - ------ + ------------------------|*atan|-- + ------ - ------------------------|*atan|-- + ------ + ------------------------|
        \  10     10                10           /     \10     10                10           /     \10     10                10           /     \10     10                10           /
$$- 16 \operatorname{atan}{\left(- \frac{3}{10} + \frac{\sqrt{69}}{10} + \frac{\sqrt{2} \sqrt{89 - 3 \sqrt{69}}}{10} \right)} \operatorname{atan}{\left(\frac{3}{10} + \frac{\sqrt{69}}{10} + \frac{\sqrt{2} \sqrt{3 \sqrt{69} + 89}}{10} \right)} \operatorname{atan}{\left(- \frac{\sqrt{69}}{10} + \frac{3}{10} + \frac{\sqrt{2} \sqrt{89 - 3 \sqrt{69}}}{10} \right)} \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{3 \sqrt{69} + 89}}{10} + \frac{3}{10} + \frac{\sqrt{69}}{10} \right)}$$
-16*atan(-3/10 + sqrt(69)/10 + sqrt(2)*sqrt(89 - 3*sqrt(69))/10)*atan(3/10 - sqrt(69)/10 + sqrt(2)*sqrt(89 - 3*sqrt(69))/10)*atan(3/10 + sqrt(69)/10 - sqrt(2)*sqrt(89 + 3*sqrt(69))/10)*atan(3/10 + sqrt(69)/10 + sqrt(2)*sqrt(89 + 3*sqrt(69))/10)
Respuesta numérica [src]
x1 = 32.1400766289699
x2 = -982.594350480533
x3 = 22.7152986682005
x4 = -40.1165544035954
x5 = -79.6227371030873
x6 = 58.6073396548636
x7 = -98.4722930246261
x8 = -26.2156619920609
x9 = -24.4085911356464
x10 = -18.1254058284668
x11 = -77.8156662466729
x12 = 3.86574274666173
x13 = 8.34185719742687
x14 = -51.3484032207792
x15 = 60.414410511278
x16 = -68.3908882859035
x17 = 99.4480441515309
x18 = 33.4745984261452
x19 = -63.9147738351384
x20 = 96.3064514979411
x21 = -71.5324809394933
x22 = 16.4321133610209
x23 = -222.328928311803
x24 = -95.3307003710363
x25 = 38.4232619361495
x26 = -33.8333690964158
x27 = 25.8568913217903
x28 = -4.2245134169323
x29 = 0.724150093071939
x30 = 69.8391884720474
x31 = -90.3820368610321
x32 = -7.3661060705221
x33 = -27.5501837892362
x34 = 47.8480398969188
x35 = -10.5076987241119
x36 = -5.55903521410765
x37 = -41.9236252600098
x38 = 17.7666351581962
x39 = 91.8303370471759
x40 = 54.1312252040984
x41 = -49.5413323643648
x42 = 61.7489323084534
x43 = -46.399739710775
x44 = 2.05867189024728
x45 = 98.1135223543555
x46 = 66.6975958184576
x47 = -65.2492956323137
x48 = -21.2669984820566
x49 = 19.5737060146107
x50 = 44.706447243329
x51 = -29.3572546456506
x52 = 82.4055590864066
x53 = 36032.9848159116
x54 = -11.8422205212872
x55 = 2229.44786328541
x56 = 90.0232661907615
x57 = 88.6887443935861
x58 = -85.9059224102669
x59 = -55.8245176715443
x60 = -70.197959142318
x61 = -2.41744256051785
x62 = -35.6404399528302
x63 = 76.122373779227
x64 = -93.5236295146219
x65 = -48.2068105671894
x66 = 63.5560031648678
x67 = 11.4834498510167
x68 = -62.1077029787239
x69 = 24.0498204653758
x70 = 68.0321176156329
x71 = 130.863970687429
x72 = 36.616191079735
x73 = -87.2404442074423
x74 = -32.4988472992404
x75 = -84.0988515538525
x76 = -19.9324766848813
x77 = 30.3330057725554
x78 = 55.4657470012738
x79 = -54.489995874369
x80 = -73.3395517959078
x81 = -99.8068148218014
x82 = 39.7577837333248
x83 = 14.6250425046065
x84 = -43.2581470571852
x85 = 52.324154347684
x86 = -13.6492913777017
x87 = -57.6315885279588
x88 = 10.1489280538413
x89 = 80.5984882299921
x90 = -76.4811444494975
x91 = 74.3153029228125
x92 = -92.1891077174465
x93 = 46.0409690405044
x94 = 83.7400808835819
x95 = 41.5648545897392
x96 = 77.4568955764023
x96 = 77.4568955764023