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sin(-x/3)+1=2 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
   /-x \        
sin|---| + 1 = 2
   \ 3 /        
$$\sin{\left(\frac{\left(-1\right) x}{3} \right)} + 1 = 2$$
Solución detallada
Tenemos la ecuación
$$\sin{\left(\frac{\left(-1\right) x}{3} \right)} + 1 = 2$$
es la ecuación trigonométrica más simple
Dividamos ambos miembros de la ecuación en -1

La ecuación se convierte en
$$\sin{\left(\frac{x}{3} \right)} = -1$$
Esta ecuación se reorganiza en
$$\frac{x}{3} = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$\frac{x}{3} = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
O
$$\frac{x}{3} = 2 \pi n - \frac{\pi}{2}$$
$$\frac{x}{3} = 2 \pi n + \frac{3 \pi}{2}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$\frac{1}{3}$$
obtenemos la respuesta:
$$x_{1} = 6 \pi n - \frac{3 \pi}{2}$$
$$x_{2} = 6 \pi n + \frac{9 \pi}{2}$$
Gráfica
Suma y producto de raíces [src]
suma
  3*pi   9*pi
- ---- + ----
   2      2  
$$- \frac{3 \pi}{2} + \frac{9 \pi}{2}$$
=
3*pi
$$3 \pi$$
producto
-3*pi 9*pi
-----*----
  2    2  
$$- \frac{3 \pi}{2} \frac{9 \pi}{2}$$
=
      2
-27*pi 
-------
   4   
$$- \frac{27 \pi^{2}}{4}$$
-27*pi^2/4
Respuesta rápida [src]
     -3*pi
x1 = -----
       2  
$$x_{1} = - \frac{3 \pi}{2}$$
     9*pi
x2 = ----
      2  
$$x_{2} = \frac{9 \pi}{2}$$
x2 = 9*pi/2
Respuesta numérica [src]
x1 = -80.1106111588322
x2 = -61.2610570017434
x3 = 51.8362773664247
x4 = 70.6858353577546
x5 = -42.411501460893
x6 = 51.8362798839346
x7 = 32.9867233840103
x8 = -98.9601680902976
x9 = -4.71238845524301
x10 = 89.5353891331438
x11 = 51.8362789040765
x12 = -42.4115005778798
x13 = 32.9867224232349
x14 = 70.6858344740862
x15 = 14.1371665638329
x16 = -80.1106140804049
x17 = -23.5619441460216
x18 = 89.5353921684403
x19 = 70.6858331755052
x20 = 70.6858338911042
x21 = -42.4114988767471
x22 = 51.8362773818419
x23 = -23.5619434901217
x24 = -80.110611523969
x25 = -23.5619461984625
x26 = -23.5619434738021
x27 = -61.2610578317089
x28 = -23.5619464082898
x29 = -42.4115021671282
x30 = -42.4114992857075
x31 = 14.1371684115644
x32 = -61.2610582787117
x33 = -42.4114999779636
x34 = -80.1106134301082
x35 = -4.71238948689267
x36 = -42.4115023072805
x37 = 14.1371682432467
x38 = -61.2610574882809
x39 = -61.2610561157384
x40 = 89.5353908982368
x41 = 183.783173900171
x42 = -23.5619482920391
x43 = -287.45572872034
x44 = 89.5353917263916
x45 = -4.71238859426546
x46 = -80.1106140658652
x47 = 89.5353892972875
x48 = 32.9867216931265
x49 = 89.5353900126591
x50 = -4.71238779907246
x51 = -98.9601688529851
x52 = 14.1371671114619
x53 = 70.6858361981262
x54 = 51.8362780425465
x55 = -80.1106089100043
x56 = 51.8362797759315
x57 = 51.8362823163449
x58 = -80.1106125777448
x59 = 32.986722491348
x60 = -23.5619458805467
x61 = -4.71239024216915
x62 = 51.8362802985196
x63 = -4.71239050808881
x64 = 14.1371660778537
x65 = 89.5353914041279
x66 = -61.2610582551732
x67 = -23.5619459803956
x68 = 14.1371656532869
x69 = -98.9601689835803
x70 = 32.986722548861
x71 = 14.1371678181509
x72 = 70.6858329020223
x73 = 14.1371654793596
x74 = -61.2610552425571
x75 = -42.4114997427582
x76 = -98.960167330773
x77 = -4.71238743209195
x78 = 70.6858336375702
x79 = 32.9867241354141
x80 = -4.71238861603651
x81 = 32.9867243978937
x82 = -98.9601670486134
x83 = -80.1106116945809
x84 = 32.9867213216468
x85 = -61.261055404731
x86 = 70.6858360595363
x87 = 89.5353922692829
x88 = -23.56194501223
x88 = -23.56194501223