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cos^2x-3sinxcosx+1=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   2                             
cos (x) - 3*sin(x)*cos(x) + 1 = 0
$$\left(- 3 \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)}\right) + 1 = 0$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
     -3*pi
x1 = -----
       4
$$x_{1} = - \frac{3 \pi}{4}$$ 
     pi
x2 = --
     4
$$x_{2} = \frac{\pi}{4}$$ 
            /      ___\
            |1   \/ 5 |
x3 = -2*atan|- - -----|
            \2     2  /
$$x_{3} = - 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)}$$ 
            /      ___\
            |1   \/ 5 |
x4 = -2*atan|- + -----|
            \2     2  /
$$x_{4} = - 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}$$ 
x4 = -2*atan(1/2 + sqrt(5)/2)
Suma y producto de raíces [src] 
suma
                    /      ___\         /      ___\
  3*pi   pi         |1   \/ 5 |         |1   \/ 5 |
- ---- + -- - 2*atan|- - -----| - 2*atan|- + -----|
   4     4          \2     2  /         \2     2  /
$$- 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} + \left(\left(- \frac{3 \pi}{4} + \frac{\pi}{4}\right) - 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)}\right)$$ 
=
        /      ___\         /      ___\     
        |1   \/ 5 |         |1   \/ 5 |   pi
- 2*atan|- + -----| - 2*atan|- - -----| - --
        \2     2  /         \2     2  /   2
$$- 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} - \frac{\pi}{2} - 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)}$$ 
producto
                /      ___\        /      ___\
-3*pi pi        |1   \/ 5 |        |1   \/ 5 |
-----*--*-2*atan|- - -----|*-2*atan|- + -----|
  4   4         \2     2  /        \2     2  /
$$- \frac{3 \pi}{4} \frac{\pi}{4} \left(- 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)}\right) \left(- 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}\right)$$ 
=
           /      ___\     /      ___\
     2     |1   \/ 5 |     |1   \/ 5 |
-3*pi *atan|- + -----|*atan|- - -----|
           \2     2  /     \2     2  /
--------------------------------------
                  4
$$- \frac{3 \pi^{2} \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)} \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}}{4}$$ 
-3*pi^2*atan(1/2 + sqrt(5)/2)*atan(1/2 - sqrt(5)/2)/4
Respuesta numérica [src] 
x1 = -36.9137136796801
x2 = -2.0344439357957
x3 = -74.2910749683609
x4 = -68.0078896611814
x5 = -20.8839998573345
x6 = 63.93900178959
x7 = -99.7455667514759
x8 = -140.264520693747
x9 = 22.776546738526
x10 = 7.39033402497368
x11 = 1.10714871779409
x12 = -65.1880475619882
x13 = 82.4668071567321
x14 = 38.484510006475
x15 = 7.06858347057703
x16 = -40550.5708238193
x17 = -77.7544181763474
x18 = 95.3549283254879
x19 = -5.49778714378214
x20 = 73.0420291959627
x21 = 67.0805944431797
x22 = 76.1836218495525
x23 = 54.1924732744239
x24 = -193.671595804773
x25 = 85.9301503647185
x26 = 26.2398899465124
x27 = 70.2221870967695
x28 = 51.0508806208341
x29 = -33.7721210260903
x30 = 48.231038521641
x31 = 10.2101761241668
x32 = -14.6008145501549
x33 = -87.1791961371168
x34 = -40330.659338068
x35 = 23.0982972929226
x36 = 0.785398163397448
x37 = -86.8574455827201
x38 = -39.7335557788732
x39 = 4.24874137138388
x40 = 73.3637797503593
x41 = 88.7499924639117
x42 = -8.31762924297529
x43 = -30.3087778181038
x44 = 51.3726311752308
x45 = 98.174770424681
x46 = 35.6646679072818
x47 = -14.9225651045515
x48 = -58.583111700412
x49 = -89.9990382363099
x50 = -17.7424072037447
x51 = 29.0597320457056
x52 = -96.2822235434895
x53 = 16.4933614313464
x54 = 57.6558164824104
x55 = -80.8960108299372
x56 = 41.9478532144614
x57 = -93.4623814442964
x58 = -80.5742602755405
x59 = -74.6128255227576
x60 = 1279.41360817444
x61 = -55.7632696012188
x62 = 13.6735193321533
x63 = 129.590696960579
x64 = -36.5919631252834
x65 = -27.4889357189107
x66 = -300.485746026826
x67 = 79.6469650575389
x68 = 44.7676953136546
x69 = 95.0331777710912
x70 = 29.3814826001022
x71 = 4958.54035608249
x72 = -61.7247043540018
x73 = -11.7809724509617
x74 = -46.0167410860528
x75 = -24.0255925109243
x76 = -64.8662970075916
x77 = -71.4712328691678
x78 = 32.2013246992954
x79 = 19.9567046393328
x80 = 92.2133356718981
x81 = -49.4800842940392
x82 = 13.3517687777566
x83 = -42.875148432463
x84 = 390.342887208532
x85 = -43.1968989868597
x86 = 60.4756585816035
x87 = -58.9048622548086
x88 = -52.2999263932324
x89 = 66.7588438887831
x90 = -21.2057504117311
x90 = -21.2057504117311
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