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(53cos^2(x)+45cos(x))/(45tg(x)-28)=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
      2                   
53*cos (x) + 45*cos(x)    
---------------------- = 0
    45*tan(x) - 28        
$$\frac{53 \cos^{2}{\left(x \right)} + 45 \cos{\left(x \right)}}{45 \tan{\left(x \right)} - 28} = 0$$
Gráfica
Suma y producto de raíces [src]
suma
pi   3*pi       /-45 \
-- + ---- + acos|----|
2     2         \ 53 /
$$\operatorname{acos}{\left(- \frac{45}{53} \right)} + \left(\frac{\pi}{2} + \frac{3 \pi}{2}\right)$$
=
           /-45 \
2*pi + acos|----|
           \ 53 /
$$\operatorname{acos}{\left(- \frac{45}{53} \right)} + 2 \pi$$
producto
pi 3*pi     /-45 \
--*----*acos|----|
2   2       \ 53 /
$$\frac{\pi}{2} \frac{3 \pi}{2} \operatorname{acos}{\left(- \frac{45}{53} \right)}$$
=
    2     /-45 \
3*pi *acos|----|
          \ 53 /
----------------
       4        
$$\frac{3 \pi^{2} \operatorname{acos}{\left(- \frac{45}{53} \right)}}{4}$$
3*pi^2*acos(-45/53)/4
Respuesta rápida [src]
     pi
x1 = --
     2 
$$x_{1} = \frac{\pi}{2}$$
     3*pi
x2 = ----
      2  
$$x_{2} = \frac{3 \pi}{2}$$
         /-45 \
x3 = acos|----|
         \ 53 /
$$x_{3} = \operatorname{acos}{\left(- \frac{45}{53} \right)}$$
x3 = acos(-45/53)
Respuesta numérica [src]
x1 = 51.836278844416
x2 = -91.6627862721142
x3 = -76.9690193349808
x4 = -70.6858342399625
x5 = 77.9832170217346
x6 = -32.9867224249878
x7 = -79.0964156577551
x8 = -80.110612610701
x9 = 42.4115007404008
x10 = -61.2610574300194
x11 = 4.71238884293985
x12 = -60.2468597362163
x13 = -23.5619450652378
x14 = -58.1194639882036
x15 = -47.6804891218571
x16 = 48.6946870370305
x17 = -9.9813772787796
x18 = -85.3796009649346
x19 = -1.57079641624667
x20 = 70.685834156145
x21 = 65.4168464073754
x22 = 67.5442423756109
x23 = -16.2645625859592
x24 = 92.6769842083221
x25 = -41.3973038146775
x26 = -32.9867222149979
x27 = -95.81857586236
x28 = 59.1336611001959
x29 = -45.5530935725063
x30 = -51.836278677788
x31 = 20.4203521034272
x32 = 61.261057242843
x33 = -97.9459715792938
x34 = -14.1371668254387
x35 = 98.9601686791901
x36 = -20.4203519473209
x37 = -39.2699083059594
x38 = -89.5353907283886
x39 = 48.6946859925665
x40 = 2.58499333557957
x41 = -7.8539814731655
x42 = 61.2610566530925
x43 = 26.7035369639341
x44 = 4.71238986686041
x45 = 64.4026492712976
x46 = 17.2787600819362
x47 = 10.9955749464831
x48 = 14.1371670316025
x49 = -39.2699073022859
x50 = 27.7177345642979
x51 = -26.703537078998
x52 = 29.8451303370772
x53 = 40.2841051786571
x54 = 54.9778721081297
x55 = -17.2787602313332
x56 = -83.2522054540344
x57 = 80.1106137044926
x58 = -66.5300450433959
x59 = 84.2664023289142
x60 = 95.8185759939645
x61 = 92.6769831428434
x62 = -64.402649108831
x63 = 83.2522048654439
x64 = -29.8451301337053
x65 = 10.9955745648126
x66 = -73.8274272996903
x67 = -3.69819197160002
x68 = 54.9778716057136
x69 = 23.56194521416
x70 = 86.393797897452
x71 = 34.0009198714775
x72 = 71.700031714555
x73 = 98.9601692699687
x74 = 48.6946852825464
x75 = -76.9690193763376
x76 = -53.9636744290367
x77 = -22.5477478931388
x78 = 7.8539816937573
x79 = -67.5442422347564
x80 = -83.2522044704987
x81 = 73.8274274994016
x82 = 21.4345492571183
x83 = 46.5672904858367
x84 = -36.1283154579461
x84 = -36.1283154579461