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sin(x-pi/3)=-1

sin(x-pi/3)=-1 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

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

La ecuación se convierte en
$$\cos{\left(x + \frac{\pi}{6} \right)} = 1$$
Esta ecuación se reorganiza en
$$x + \frac{\pi}{6} = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$x + \frac{\pi}{6} = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
O
$$x + \frac{\pi}{6} = \pi n$$
$$x + \frac{\pi}{6} = \pi n - \pi$$
, donde n es cualquier número entero
Transportemos
$$\frac{\pi}{6}$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$x = \pi n - \frac{\pi}{6}$$
$$x = \pi n - \frac{7 \pi}{6}$$
Gráfica
Suma y producto de raíces [src]
suma
  pi   11*pi
- -- + -----
  6      6  
$$- \frac{\pi}{6} + \frac{11 \pi}{6}$$
=
5*pi
----
 3  
$$\frac{5 \pi}{3}$$
producto
-pi  11*pi
----*-----
 6     6  
$$- \frac{\pi}{6} \frac{11 \pi}{6}$$
=
      2
-11*pi 
-------
   36  
$$- \frac{11 \pi^{2}}{36}$$
-11*pi^2/36
Respuesta rápida [src]
     -pi 
x1 = ----
      6  
$$x_{1} = - \frac{\pi}{6}$$
     11*pi
x2 = -----
       6  
$$x_{2} = \frac{11 \pi}{6}$$
x2 = 11*pi/6
Respuesta numérica [src]
x1 = -25.6563400637071
x2 = 100.007366129962
x3 = -0.523599258250701
x4 = -101.054563229573
x5 = 49.7418838493326
x6 = 301.069297155331
x7 = -6.80678449725847
x8 = 68.5914401276649
x9 = -13.0899698146708
x10 = 49.7418835245054
x11 = 93.7241806097162
x12 = 37.1755126583087
x13 = 62.3082540196632
x14 = -19.373154896527
x15 = 87.4409958250878
x16 = -94.7713780045959
x17 = 56.0250690081558
x18 = 18.3259568926578
x19 = 43.4586978952293
x20 = -25.6563402322524
x21 = -50.7890816527148
x22 = -75.9218220581853
x23 = 37.1755134637125
x24 = 56.0250693524419
x25 = 30.8923282331952
x26 = -264.417382419922
x27 = 93.7241810081872
x28 = -13.0899697075722
x29 = 62.308254257502
x30 = -57.0722665843695
x31 = -88.4881935647341
x32 = -19.3731541846809
x33 = -69.6386373548543
x34 = -50.7890808483935
x35 = 5.75958669034246
x36 = 49.7418831724391
x37 = 56.0250689522333
x38 = -75.9218229143423
x39 = -69.6386366485818
x40 = 12.0427713725902
x41 = -88.4881928048828
x42 = -6.80678369229017
x43 = -44.5058964115732
x44 = 30.8923274298613
x45 = 100.007365661841
x46 = 56.0250685169442
x47 = -31.939525771185
x48 = 68.5914401180933
x49 = 68.5914394200902
x50 = -57.0722668645673
x51 = -57.0722660751833
x52 = -94.7713788080582
x53 = 43.4586986677198
x54 = -31.9395254617805
x55 = 81.1578106196128
x56 = 87.4409950488631
x57 = 74.8746253871791
x58 = -69.638637223832
x59 = 30.8923274495049
x60 = -82.2050076281063
x61 = -44.5058956472658
x62 = -38.2227106630569
x63 = -82.2050077643523
x64 = -82.2050082777704
x65 = 93.7241803230185
x66 = 24.6091430772094
x67 = 156.556034516879
x68 = -38.2227111279653
x69 = -13.0899689209265
x70 = 81.1578098139843
x71 = -0.523598489731523
x72 = -31.9395249202358
x73 = 18.3259570967149
x74 = 62.3082547928689
x75 = -19.3731539653969
x76 = 81.1578093180369
x77 = -88.4881942807791
x78 = 12.0427717615073
x79 = -25.65633950106
x80 = 74.8746246066628
x81 = -75.9218228126903
x82 = 24.6091422617441
x83 = 12.0427722166701
x84 = -44.5058967203222
x85 = 18.3259576460966
x86 = -63.3554510011992
x87 = -38.2227104687978
x88 = -63.3554520547243
x89 = 24.6091429668081
x90 = 5.75958602210796
x91 = 5.75958643339931
x92 = -63.3554513363679
x93 = 5.75958726070503
x93 = 5.75958726070503
Gráfico
sin(x-pi/3)=-1 la ecuación