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(89cos^2+80cosx)/(80tgx-39)=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
      2                   
89*cos (x) + 80*cos(x)    
---------------------- = 0
    80*tan(x) - 39        
$$\frac{89 \cos^{2}{\left(x \right)} + 80 \cos{\left(x \right)}}{80 \tan{\left(x \right)} - 39} = 0$$
Gráfica
Suma y producto de raíces [src]
suma
pi   3*pi       /-80 \
-- + ---- + acos|----|
2     2         \ 89 /
$$\operatorname{acos}{\left(- \frac{80}{89} \right)} + \left(\frac{\pi}{2} + \frac{3 \pi}{2}\right)$$
=
           /-80 \
2*pi + acos|----|
           \ 89 /
$$\operatorname{acos}{\left(- \frac{80}{89} \right)} + 2 \pi$$
producto
pi 3*pi     /-80 \
--*----*acos|----|
2   2       \ 89 /
$$\frac{\pi}{2} \frac{3 \pi}{2} \operatorname{acos}{\left(- \frac{80}{89} \right)}$$
=
    2     /-80 \
3*pi *acos|----|
          \ 89 /
----------------
       4        
$$\frac{3 \pi^{2} \operatorname{acos}{\left(- \frac{80}{89} \right)}}{4}$$
3*pi^2*acos(-80/89)/4
Respuesta rápida [src]
     pi
x1 = --
     2 
$$x_{1} = \frac{\pi}{2}$$
     3*pi
x2 = ----
      2  
$$x_{2} = \frac{3 \pi}{2}$$
         /-80 \
x3 = acos|----|
         \ 89 /
$$x_{3} = \operatorname{acos}{\left(- \frac{80}{89} \right)}$$
x3 = acos(-80/89)
Respuesta numérica [src]
x1 = -20.4203519350848
x2 = 61.261057281939
x3 = 64.4026492759742
x4 = 23.5619452273858
x5 = 54.977871880111
x6 = -7.85398146954404
x7 = -53.8606728071343
x8 = 86.3937978985905
x9 = -76.969019298181
x10 = 90.6525892579962
x11 = 2.68799495748202
x12 = 70.6858342181557
x13 = 48.694687254321
x14 = -26.7035371837917
x15 = -83.2522054408333
x16 = 92.6769831513431
x17 = -39.2699071084088
x18 = -23.561945057928
x19 = -36.1283154534398
x20 = 78.0862186436371
x21 = 54.9778721995257
x22 = 20.42035210933
x23 = -89.5353907261229
x24 = 34.10392149338
x25 = 36.1283158828592
x26 = 21.5375508790208
x27 = -22.4447462712363
x28 = 52.9534774149187
x29 = 65.5198480292779
x30 = -60.1438581143138
x31 = -1.57079641458582
x32 = 95.8185760019554
x33 = -73.827427297917
x34 = -67.5442422258415
x35 = -61.2610573388404
x36 = -66.4270434214934
x37 = 7.85398169925954
x38 = -14.1371668236416
x39 = -9.87837565687715
x40 = 10.9955749926126
x41 = 26.7035370344727
x42 = -45.5530944158358
x43 = 73.8274275020169
x44 = 17.2787601189069
x45 = -95.8185758615757
x46 = 67.5442423898738
x47 = -29.8451301305455
x48 = 51.8362788510575
x49 = -80.1106126070864
x50 = 84.3694039508166
x51 = -51.836278676125
x52 = 8.97118026466161
x53 = 4.71239007204449
x54 = 46.6702921077391
x55 = -97.8429699573914
x56 = 29.8451303392676
x57 = 42.4115007417902
x58 = -70.6858342069648
x59 = 48.6946860019923
x60 = -83.2522042871984
x61 = 4.71238885343013
x62 = -39.269908294228
x63 = -32.986722132658
x64 = -91.5597846502118
x65 = 98.9601693662686
x66 = -3.59519034969756
x67 = 71.8030333364575
x68 = -17.2787601511316
x69 = -16.1615609640567
x70 = 14.1371670371979
x71 = 59.2366627220983
x72 = -58.1194639867683
x73 = 27.8207361862004
x74 = 98.9601688622315
x75 = 40.3871068005595
x76 = -47.5774874999547
x77 = 10.9955750332311
x78 = -64.4026490975388
x79 = -45.5530935705535
x80 = -26.7035370440585
x81 = -86.393798542577
x81 = -86.393798542577