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sin(-x/2)=1 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

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

La ecuación se convierte en
$$\sin{\left(\frac{x}{2} \right)} = -1$$
Esta ecuación se reorganiza en
$$\frac{x}{2} = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$\frac{x}{2} = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
O
$$\frac{x}{2} = 2 \pi n - \frac{\pi}{2}$$
$$\frac{x}{2} = 2 \pi n + \frac{3 \pi}{2}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$\frac{1}{2}$$
obtenemos la respuesta:
$$x_{1} = 4 \pi n - \pi$$
$$x_{2} = 4 \pi n + 3 \pi$$
Gráfica
Suma y producto de raíces [src]
suma
-pi + 3*pi
$$- \pi + 3 \pi$$
=
2*pi
$$2 \pi$$
producto
-pi*3*pi
$$- \pi 3 \pi$$
=
     2
-3*pi 
$$- 3 \pi^{2}$$
-3*pi^2
Respuesta rápida [src]
x1 = -pi
$$x_{1} = - \pi$$
x2 = 3*pi
$$x_{2} = 3 \pi$$
x2 = 3*pi
Respuesta numérica [src]
x1 = -40.840705514174
x2 = -3.1415920909332
x3 = 59.6902597628977
x4 = -28.2743333728019
x5 = 97.3893725976594
x6 = 59.6902594160982
x7 = 21.9911476515378
x8 = -40.8407057343968
x9 = 84.8230013528861
x10 = -53.407074099621
x11 = 21.9911485852083
x12 = -91.1061866269766
x13 = -3.14159244591793
x14 = 47.1238883520716
x15 = -15.7079641216365
x16 = -91.1061893000426
x17 = 9.42477785524033
x18 = 84.8230022236836
x19 = 21.9911493543639
x20 = -91.1061879410652
x21 = 34.5575190198289
x22 = -28.2743336521146
x23 = -103.672556618325
x24 = -3.14159363499305
x25 = 34.5575198674508
x26 = -15.7079640213661
x27 = 72.2566318142828
x28 = -28.2743345506996
x29 = -65.9734467103803
x30 = 47.1238887891963
x31 = -91.10618728017
x32 = 84.8230026783574
x33 = -91.1061864056832
x34 = -65.9734464982309
x35 = 47.1238897245433
x36 = 21.9911478139095
x37 = 84.8230017459365
x38 = -65.9734448735059
x39 = 59.6902591286344
x40 = -40.8407049390955
x41 = -53.4070752977589
x42 = -40.840702830856
x43 = -28.2743348785101
x44 = -65.9734449211945
x45 = -40.8407040589859
x46 = -78.5398173635881
x47 = 9.42477894916069
x48 = -28.2743329527591
x49 = -3.1415950208335
x50 = -65.9734466347336
x51 = 97.3893732551872
x52 = -65.9734457649054
x53 = 72.2566302523232
x54 = -91.1061859213063
x55 = -103.672558275184
x56 = -78.5398169064311
x57 = 9.42477828111644
x58 = 34.5575187273286
x59 = 34.5575201953822
x60 = -78.5398160355522
x61 = -40.8407034751919
x62 = 9.4247774082407
x63 = 21.9911494370191
x64 = -40.8407043325125
x65 = 47.1238893765929
x66 = -15.7079632966168
x67 = 59.6902606135717
x68 = -15.7079623299946
x69 = 47.123890256687
x70 = 59.6902613557236
x71 = -3.14159389871743
x72 = -53.4070760410661
x73 = 34.5575182674959
x74 = 97.3893712357817
x75 = -15.7079624977706
x76 = -53.4070744460719
x77 = 72.2566310277173
x78 = 97.3893735581761
x79 = 59.6902608771019
x80 = 72.2566319571987
x81 = 9.42477693583124
x82 = 47.123891242423
x83 = -3.14159296369468
x84 = -28.2743337045464
x85 = 72.2566301889781
x86 = 84.8230006713996
x87 = -53.4070755183111
x88 = -78.5398153571806
x89 = -78.5398163457967
x90 = 97.3893717230424
x91 = 34.5575202880375
x92 = 47.1238908281958
x93 = -3.14159162121992
x93 = -3.14159162121992