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4*(cos(x))^3+3*cos(x)+4*3^(1/2)=4*3^(1/2)*(sin(x))^2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
     3                     ___       ___    2   
4*cos (x) + 3*cos(x) + 4*\/ 3  = 4*\/ 3 *sin (x)
$$\left(4 \cos^{3}{\left(x \right)} + 3 \cos{\left(x \right)}\right) + 4 \sqrt{3} = 4 \sqrt{3} \sin^{2}{\left(x \right)}$$
Gráfica
Respuesta rápida [src]
     -pi 
x1 = ----
      2  
$$x_{1} = - \frac{\pi}{2}$$
     pi
x2 = --
     2 
$$x_{2} = \frac{\pi}{2}$$
            /   _____________\
            |  /         ___ |
x3 = -2*atan\\/  7 + 4*\/ 3  /
$$x_{3} = - 2 \operatorname{atan}{\left(\sqrt{4 \sqrt{3} + 7} \right)}$$
           /   _____________\
           |  /         ___ |
x4 = 2*atan\\/  7 + 4*\/ 3  /
$$x_{4} = 2 \operatorname{atan}{\left(\sqrt{4 \sqrt{3} + 7} \right)}$$
x4 = 2*atan(sqrt(4*sqrt(3) + 7))
Suma y producto de raíces [src]
suma
                  /   _____________\         /   _____________\
  pi   pi         |  /         ___ |         |  /         ___ |
- -- + -- - 2*atan\\/  7 + 4*\/ 3  / + 2*atan\\/  7 + 4*\/ 3  /
  2    2                                                       
$$\left(- 2 \operatorname{atan}{\left(\sqrt{4 \sqrt{3} + 7} \right)} + \left(- \frac{\pi}{2} + \frac{\pi}{2}\right)\right) + 2 \operatorname{atan}{\left(\sqrt{4 \sqrt{3} + 7} \right)}$$
=
0
$$0$$
producto
               /   _____________\       /   _____________\
-pi  pi        |  /         ___ |       |  /         ___ |
----*--*-2*atan\\/  7 + 4*\/ 3  /*2*atan\\/  7 + 4*\/ 3  /
 2   2                                                    
$$- \frac{\pi}{2} \frac{\pi}{2} \left(- 2 \operatorname{atan}{\left(\sqrt{4 \sqrt{3} + 7} \right)}\right) 2 \operatorname{atan}{\left(\sqrt{4 \sqrt{3} + 7} \right)}$$
=
         /   _____________\
  2     2|  /         ___ |
pi *atan \\/  7 + 4*\/ 3  /
$$\pi^{2} \operatorname{atan}^{2}{\left(\sqrt{4 \sqrt{3} + 7} \right)}$$
pi^2*atan(sqrt(7 + 4*sqrt(3)))^2
Respuesta numérica [src]
x1 = 54.9778714378214
x2 = -98.9601685880785
x3 = 53.9306739067582
x4 = -4.71238898038469
x5 = -14.1371669411541
x6 = -27.7507351061618
x7 = 22.5147474023572
x8 = 39.2699081698724
x9 = 23.5619449019235
x10 = 97.9129711187936
x11 = 73.8274273593601
x12 = 84.299402835909
x13 = -20.4203522483337
x14 = -26.7035375555132
x15 = -54.9778714378214
x16 = 78.0162175404203
x17 = 53.9306739542935
x18 = -95.8185759344887
x19 = 40.3171056734306
x20 = 26.7035375555132
x21 = 90.5825879890888
x22 = -3.66519148884796
x23 = 17.2787595947439
x24 = 20.4203522483337
x25 = -92.6769832808989
x26 = -84.2994026731556
x27 = 10.9955742875643
x28 = 90.5825877161083
x29 = 67.5442420521806
x30 = 36.1283155162826
x31 = 76.9690200129499
x32 = 58.1194640914112
x33 = -29.845130209103
x34 = -41.3643031602587
x35 = 61.261056745001
x36 = 3.66519181835324
x37 = 41.3643042050554
x38 = 2.61799406300696
x39 = -21.4675496339111
x40 = -85.3466006129319
x41 = -40.3171058924496
x42 = 47.6474884275061
x43 = -60.2138591525219
x44 = -71.7330322686084
x45 = 70.6858347057703
x46 = 80.1106126665397
x47 = 34.0339203480596
x48 = -78.0162168822159
x49 = 16.2315620586014
x50 = 46.6002908355196
x51 = -53.9306744027422
x52 = 14.1371669411541
x53 = -46.6002904367904
x54 = -67.5442420521806
x55 = 91.6297859344981
x56 = -41.3643034660035
x57 = -78.0162175458364
x58 = -16.2315620184538
x59 = -91.6297858128015
x60 = -84.2994029194441
x61 = 9.94837775624436
x62 = 46.6002911447523
x63 = -58.1194640914112
x64 = 83.2522053201295
x65 = 96.8657737226645
x66 = 2.61799368367998
x67 = -32.9867228626928
x68 = -70.6858347057703
x69 = -91.6297856658222
x70 = -17.2787595947439
x71 = -65.4498466211443
x72 = -39.2699081698724
x73 = -40.317105518949
x74 = -47.6474886509289
x75 = 60.2138592265139
x76 = -64.4026493985908
x77 = -51.8362787842316
x78 = 27.7507351026045
x79 = 3.66519163388085
x80 = -61.261056745001
x81 = -73.8274273593601
x82 = 29.845130209103
x83 = -9.94837688843499
x84 = 86.3937979737193
x85 = 64.4026493985908
x86 = 47.6474887851224
x87 = 9.94837678887681
x88 = 98.9601685880785
x89 = -48.6946861306418
x90 = 71.7330321957952
x91 = -23.5619449019235
x92 = -34.0339203777002
x93 = -76.9690200129499
x94 = -78.0162169427699
x95 = 32.9867228626928
x96 = -10.9955742875643
x97 = 66.4970445003389
x98 = -80.1106126665397
x99 = -7.85398163397448
x99 = -7.85398163397448