Sr Examen

Otras calculadoras

((25cos^2x)+24cosx)/(24tgx−7)=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
      2                   
25*cos (x) + 24*cos(x)    
---------------------- = 0
    24*tan(x) - 7         
$$\frac{25 \cos^{2}{\left(x \right)} + 24 \cos{\left(x \right)}}{24 \tan{\left(x \right)} - 7} = 0$$
Gráfica
Respuesta rápida [src]
     pi
x1 = --
     2 
$$x_{1} = \frac{\pi}{2}$$
     3*pi
x2 = ----
      2  
$$x_{2} = \frac{3 \pi}{2}$$
         /-24 \
x3 = acos|----|
         \ 25 /
$$x_{3} = \operatorname{acos}{\left(- \frac{24}{25} \right)}$$
x3 = acos(-24/25)
Suma y producto de raíces [src]
suma
pi   3*pi       /-24 \
-- + ---- + acos|----|
2     2         \ 25 /
$$\operatorname{acos}{\left(- \frac{24}{25} \right)} + \left(\frac{\pi}{2} + \frac{3 \pi}{2}\right)$$
=
           /-24 \
2*pi + acos|----|
           \ 25 /
$$\operatorname{acos}{\left(- \frac{24}{25} \right)} + 2 \pi$$
producto
pi 3*pi     /-24 \
--*----*acos|----|
2   2       \ 25 /
$$\frac{\pi}{2} \frac{3 \pi}{2} \operatorname{acos}{\left(- \frac{24}{25} \right)}$$
=
    2     /-24 \
3*pi *acos|----|
          \ 25 /
----------------
       4        
$$\frac{3 \pi^{2} \operatorname{acos}{\left(- \frac{24}{25} \right)}}{4}$$
3*pi^2*acos(-24/25)/4
Respuesta numérica [src]
x1 = -89.5353914627451
x2 = -9.70857206997771
x3 = -34.8413132986961
x4 = -73.8274272954207
x5 = 40.556910387459
x6 = 89.5353900059161
x7 = 54.9778724001142
x8 = 26.7035371112275
x9 = 67.5442424171334
x10 = 34.2737250802794
x11 = 9.14098385156105
x12 = -76.9690191299018
x13 = -66.257239834594
x14 = -15.9917573771573
x15 = -17.2787600651216
x16 = -39.2699082698323
x17 = 71.9728369233569
x18 = -58.1194639841557
x19 = -72.5404251417736
x20 = -64.4026490761368
x21 = -1.57079641159274
x22 = 61.2610573608681
x23 = -95.8185758601251
x24 = 92.6769831678918
x25 = 70.6858342865628
x26 = 48.69468602068
x27 = 95.818576011853
x28 = -29.8451301260274
x29 = -29.8451300600032
x30 = -36.1283154476226
x31 = -51.8362786730265
x32 = 14.1371670453974
x33 = -42.4115008806599
x34 = 21.7073544659202
x35 = -26.7035369740839
x36 = 65.6896516161773
x37 = -67.5442422146661
x38 = 20.4203521168358
x39 = 73.827427506814
x40 = -61.2610572425563
x41 = -20.4203519118301
x42 = -80.1106126023974
x43 = -53.6908692202348
x44 = 23.5619452525916
x45 = -23.561945048698
x46 = -83.2522054125193
x47 = 84.5392075377161
x48 = -97.6731663704919
x49 = -45.5530935670323
x50 = 32.9867218028127
x51 = -32.9867219542796
x52 = 29.8451303432752
x53 = -10.9955754088842
x54 = 78.2560222305365
x55 = 14.1371670468135
x56 = 51.8362788594496
x57 = 64.4026492819617
x58 = 32.9867227555343
x59 = 7.85398170630351
x60 = 4.7123888746854
x61 = 58.1194643805399
x62 = -86.3937979834582
x63 = -78.8236104489532
x64 = 27.9905397730998
x65 = 86.393797900642
x66 = 42.4115007442937
x67 = -7.85398146275104
x68 = 120.951317766729
x69 = -89.535390722034
x70 = 58.1194644010617
x71 = -3.42538676279812
x72 = -59.9740545274144
x73 = 10.995575222361
x74 = -14.137166820362
x75 = -22.2749426843369
x76 = 17.2787601932431
x77 = 98.9601695790834
x78 = 45.5530931854609
x79 = 1.5707961882957
x80 = 76.9690190103066
x81 = -70.6858341411339
x81 = -70.6858341411339