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2sin2x-1/2=1 la ecuación

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Solución numérica:

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Solución

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

La ecuación se convierte en
$$\sin{\left(2 x \right)} = \frac{3}{4}$$
Esta ecuación se reorganiza en
$$2 x = 2 \pi n + \operatorname{asin}{\left(\frac{3}{4} \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(\frac{3}{4} \right)} + \pi$$
O
$$2 x = 2 \pi n + \operatorname{asin}{\left(\frac{3}{4} \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(\frac{3}{4} \right)} + \pi$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$2$$
obtenemos la respuesta:
$$x_{1} = \pi n + \frac{\operatorname{asin}{\left(\frac{3}{4} \right)}}{2}$$
$$x_{2} = \pi n - \frac{\operatorname{asin}{\left(\frac{3}{4} \right)}}{2} + \frac{\pi}{2}$$
Gráfica
Suma y producto de raíces [src]
suma
pi   asin(3/4)   asin(3/4)
-- - --------- + ---------
2        2           2    
$$\frac{\operatorname{asin}{\left(\frac{3}{4} \right)}}{2} + \left(- \frac{\operatorname{asin}{\left(\frac{3}{4} \right)}}{2} + \frac{\pi}{2}\right)$$
=
pi
--
2 
$$\frac{\pi}{2}$$
producto
/pi   asin(3/4)\ asin(3/4)
|-- - ---------|*---------
\2        2    /     2    
$$\left(- \frac{\operatorname{asin}{\left(\frac{3}{4} \right)}}{2} + \frac{\pi}{2}\right) \frac{\operatorname{asin}{\left(\frac{3}{4} \right)}}{2}$$
=
(pi - asin(3/4))*asin(3/4)
--------------------------
            4             
$$\frac{\left(\pi - \operatorname{asin}{\left(\frac{3}{4} \right)}\right) \operatorname{asin}{\left(\frac{3}{4} \right)}}{4}$$
(pi - asin(3/4))*asin(3/4)/4
Respuesta rápida [src]
     pi   asin(3/4)
x1 = -- - ---------
     2        2    
$$x_{1} = - \frac{\operatorname{asin}{\left(\frac{3}{4} \right)}}{2} + \frac{\pi}{2}$$
     asin(3/4)
x2 = ---------
         2    
$$x_{2} = \frac{\operatorname{asin}{\left(\frac{3}{4} \right)}}{2}$$
x2 = asin(3/4)/2
Respuesta numérica [src]
x1 = 28.6983649217989
x2 = -61.6850877844917
x3 = -30.9918954964072
x4 = 9.84880900026012
x5 = 53.8311061505172
x6 = -67.9682730916713
x7 = 7.42995059448374
x8 = -14.5611979806448
x9 = -17.7027906342346
x10 = -58.5434951309019
x11 = 66.3974767648764
x12 = -45.9771245165427
x13 = -52.9830440715357
x14 = -36.5523465557734
x15 = 51.4122477447408
x16 = -2.71756161409905
x17 = -34.133488149997
x18 = -74.2514583988509
x19 = 63.9786183591
x20 = -27.8503028428174
x21 = 70.2618036662796
x22 = 0.424031039490741
x23 = 78.9638473792356
x24 = -9.00074692127864
x25 = -23.9859759414142
x26 = -21.5671175356378
x27 = -96.2426069739794
x28 = 107.960915509357
x29 = 92.2529522414082
x30 = -81.2573779538439
x31 = 73.4033963198694
x32 = 12.9904016538499
x33 = 82.1054400328254
x34 = -39.6939392093632
x35 = 85.9697669342286
x36 = 60.1142914576968
x37 = 34.9815502289785
x38 = 13.7131359016633
x39 = -52.2603098237223
x40 = -30.2691612485938
x41 = 56.972698804107
x42 = -43.5582661107664
x43 = -83.6762363596203
x44 = -12.1423395748684
x45 = -71.8325999930745
x46 = -49.841451417946
x47 = 89.1113595878184
x48 = 38.1231428825683
x49 = -87.5405632610235
x50 = 57.6954330519204
x51 = 22.4151796146193
x52 = -78.1157853002541
x53 = 31.8399575753887
x54 = 75.8222547256458
x55 = 26.2795065160225
x56 = -59.2662293787153
x57 = -37.2750808035868
x58 = 100.954995954364
x59 = -93.8237485682031
x60 = 97.8134033007743
x61 = 35.7042844767919
x62 = -89.9594216667998
x63 = -15.2839322284582
x64 = 44.4063281897478
x65 = 50.6895134969274
x66 = -1.99482736628564
x67 = 4.28835794089395
x68 = 72.680662072056
x69 = -56.1246367251255
x70 = -65.5494146858949
x71 = 19.9963212088429
x72 = -8.27801267346522
x73 = -5.85915426768885
x74 = 88.3886253400049
x75 = 6.70721634667033
x76 = -84.3989706074337
x77 = 48.2706550911511
x78 = -100.106933875383
x79 = 79.686581627049
x80 = 16.1319943074397
x81 = 94.6718106471845
x82 = -80.5346437060305
x83 = 41.9874697839715
x84 = 95.3945448949979
x85 = 29.4210991696123
x85 = 29.4210991696123