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sin(x/2-pi/2)=1 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

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

La ecuación se convierte en
$$\cos{\left(\frac{x}{2} \right)} = -1$$
Esta ecuación se reorganiza en
$$\frac{x}{2} = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$\frac{x}{2} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
O
$$\frac{x}{2} = \pi n + \pi$$
$$\frac{x}{2} = \pi n$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$\frac{1}{2}$$
obtenemos la respuesta:
$$x_{1} = 2 \pi n + 2 \pi$$
$$x_{2} = 2 \pi n$$
Gráfica
Respuesta rápida [src]
x1 = 2*pi
$$x_{1} = 2 \pi$$
x1 = 2*pi
Suma y producto de raíces [src]
suma
2*pi
$$2 \pi$$
=
2*pi
$$2 \pi$$
producto
2*pi
$$2 \pi$$
=
2*pi
$$2 \pi$$
2*pi
Respuesta numérica [src]
x1 = 18.8495549415754
x2 = 18.8495561010751
x3 = 69.115037955532
x4 = 43.9822979229286
x5 = 94.2477803922665
x6 = -81.6814082319334
x7 = 69.1150373651011
x8 = -56.5486687887842
x9 = 81.681409932803
x10 = -94.2477790629797
x11 = -31.4159255258029
x12 = 94.2477805288104
x13 = -94.2477802857943
x14 = -56.548667456373
x15 = 81.6814094388795
x16 = 973.893720162307
x17 = -69.1150378269834
x18 = -6.28318627375063
x19 = 6.28318454684724
x20 = -69.115038701061
x21 = -94.2477805989545
x22 = 94.2477787666659
x23 = -56.5486683277755
x24 = -31.4159269573538
x25 = 18.8495556154405
x26 = -43.982296295854
x27 = 69.115038835587
x28 = -31.4159267183799
x29 = -69.1150380827831
x30 = 81.6814091930517
x31 = 94.2477796093523
x32 = -56.5486667805662
x33 = -43.9822971745293
x34 = 69.1150368714384
x35 = 56.5486675992574
x36 = 81.6814079898679
x37 = 43.982297169474
x38 = 18.8495569537229
x39 = 81.6814083413212
x40 = -69.115037346238
x41 = -69.1150393645777
x42 = -18.8495543136467
x43 = -18.8495572113627
x44 = 6.28318528419795
x45 = -6.28318480992034
x46 = 31.415926404003
x47 = 31.4159268602638
x48 = 56.5486681672153
x49 = -18.8495563601837
x50 = 56.5486668446775
x51 = -43.9822979202134
x52 = -81.68140804614
x53 = -31.4159267991785
x54 = 56.5486672894687
x55 = -6.28318512498487
x56 = 6.28318445599649
x57 = -81.6814097251289
x58 = -69.1150405916551
x59 = 18.8495554920234
x60 = -18.8495569383691
x61 = -81.6814098544517
x62 = 43.9822963919738
x63 = 56.5486684458067
x64 = 18.8495564877336
x65 = -31.4159258676764
x66 = 31.4159255107699
x67 = -43.9822963521153
x68 = -6.28318437561383
x69 = 69.1150397628024
x70 = -56.5486677946696
x71 = -18.8495548993085
x72 = -6.28318500560576
x73 = -18.8495554800568
x74 = -31.4159274639505
x75 = -420.973417050673
x76 = -43.9822980632848
x77 = 43.9822962232996
x78 = 81.6814069775521
x79 = 69.1150394039813
x80 = 43.9822980146158
x81 = -81.6814090382823
x82 = 94.2477788210844
x83 = 6.28318624191326
x84 = -6.28318597231491
x85 = -94.2477786842917
x86 = 31.4159259869291
x87 = 6.28318608026041
x88 = -94.2477794433785
x89 = 56.548668769019
x90 = -6.28318630492991
x91 = 31.4159275256971
x91 = 31.4159275256971