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(2*x+pi/2)*(2*sin(x))+1=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
/      pi\                 
|2*x + --|*2*sin(x) + 1 = 0
\      2 /                 
$$\left(2 x + \frac{\pi}{2}\right) 2 \sin{\left(x \right)} + 1 = 0$$
Solución detallada
Tenemos la ecuación
$$\left(2 x + \frac{\pi}{2}\right) 2 \sin{\left(x \right)} + 1 = 0$$
cambiamos
$$\left(4 x + \pi\right) \sin{\left(x \right)} = 0$$
$$\left(2 x + \frac{\pi}{2}\right) 2 \sin{\left(x \right)} = 0$$
Sustituimos
$$w = \sin{\left(x \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
2*w2*x+pi/2 = 0

Dividamos ambos miembros de la ecuación en pi + 4*x
w = 0 / (pi + 4*x)

Obtenemos la respuesta: w = 0
hacemos cambio inverso
$$\sin{\left(x \right)} = w$$
Tenemos la ecuación
$$\sin{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
O
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, donde n es cualquier número entero
sustituimos w:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$x_{1} = 2 \pi n$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
$$x_{2} = 2 \pi n + \pi$$
Gráfica
Respuesta numérica [src]
x1 = -69.1113794405577
x2 = -53.4118255938638
x3 = -87.9617265456167
x4 = -28.283425568794
x5 = -62.827823560136
x6 = 6.24763125738913
x7 = -100.52845847221
x8 = 31.408160929368
x9 = -59.6945042570114
x10 = 18.8368149140373
x11 = -94.2451046549519
x12 = -31.4077624772831
x13 = 43.9767120404713
x14 = 78.5429678027906
x15 = 28.2829344128483
x16 = 100.528497333773
x17 = 15.7231075554297
x18 = -65.9772805680613
x19 = -15.7246984339381
x20 = -78.5430314637153
x21 = 22.0021197136555
x22 = 87.9617773057274
x23 = -84.825976404761
x24 = 47.1291074541411
x25 = -25.1224686530988
x26 = -91.1089547848732
x27 = -18.8357052988526
x28 = 84.8259218256501
x29 = -9.45362292939034
x30 = 56.5443070097234
x31 = 62.8279230672197
x32 = -22.0029315557613
x33 = 91.1089074742347
x34 = 53.4116879215048
x35 = 12.5476190709496
x36 = 94.2451488716182
x37 = 97.3919186770772
x38 = -3.24347436862679
x39 = 40.8467095133832
x40 = 69.1114616727597
x41 = -97.3919600801033
x42 = 37.6926145803262
x43 = 163.36129495814
x44 = 65.9771903462855
x45 = -81.6783184831023
x46 = 9.44920732138379
x47 = 3.20429518985621
x48 = -43.9765088898535
x49 = -47.1292842848334
x50 = -12.5451099883642
x51 = 59.6943940420635
x52 = 25.1230917323275
x53 = 50.2605848928399
x54 = 72.2600535658258
x55 = -72.2601287793578
x56 = -40.8469449352619
x57 = -34.5649201906652
x58 = 75.3949419936841
x59 = -37.6923379974808
x60 = 34.5645913863171
x61 = -56.5441841512594
x62 = -6.23731377981202
x63 = -50.2604293820218
x64 = 81.6783773545165
x65 = -75.3948728990236
x65 = -75.3948728990236