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sin(pi/4-x)=1/2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
   /pi    \      
sin|-- - x| = 1/2
   \4     /      
$$\sin{\left(- x + \frac{\pi}{4} \right)} = \frac{1}{2}$$
Solución detallada
Tenemos la ecuación
$$\sin{\left(- x + \frac{\pi}{4} \right)} = \frac{1}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x + \frac{\pi}{4} = \pi n + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
$$x + \frac{\pi}{4} = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
O
$$x + \frac{\pi}{4} = \pi n + \frac{\pi}{3}$$
$$x + \frac{\pi}{4} = \pi n - \frac{2 \pi}{3}$$
, donde n es cualquier número entero
Transportemos
$$\frac{\pi}{4}$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$x = \pi n + \frac{\pi}{12}$$
$$x = \pi n - \frac{11 \pi}{12}$$
Gráfica
Suma y producto de raíces [src]
suma
pi   17*pi
-- + -----
12     12 
$$\frac{\pi}{12} + \frac{17 \pi}{12}$$
=
3*pi
----
 2  
$$\frac{3 \pi}{2}$$
producto
pi 17*pi
--*-----
12   12 
$$\frac{\pi}{12} \frac{17 \pi}{12}$$
=
     2
17*pi 
------
 144  
$$\frac{17 \pi^{2}}{144}$$
17*pi^2/144
Respuesta rápida [src]
     pi
x1 = --
     12
$$x_{1} = \frac{\pi}{12}$$
     17*pi
x2 = -----
       12 
$$x_{2} = \frac{17 \pi}{12}$$
x2 = 17*pi/12
Respuesta numérica [src]
x1 = 54.7160720500222
x2 = -58.3812634792103
x3 = -93.9859802198946
x4 = 6.54498469497874
x5 = -177.761784315622
x6 = -64.6644487863899
x7 = 17.0169602069447
x8 = -1.83259571459405
x9 = -45.8148928648512
x10 = -33.248522250492
x11 = 56.8104671524154
x12 = -37.4373124552784
x13 = -39.5317075576716
x14 = -62.5700536839967
x15 = 12.8281700021583
x16 = 81.9432083811338
x17 = -50.0036830696375
x18 = 42.1497014356631
x19 = 98.6983692002793
x20 = -83.5140047079287
x21 = -26.9653369433124
x22 = -81.4196096055355
x23 = -68.8532389911763
x24 = 50.5272818452358
x25 = -77.2308194007491
x26 = 0.261799387799149
x27 = -70.9476340935695
x28 = -18.5877565337396
x29 = 37.9609112308767
x30 = -20.6821516361328
x31 = -75.1364242983559
x32 = 73.565627971561
x33 = 92.4151838930998
x34 = 69.3768377667746
x35 = 88.2263936883134
x36 = -100.269165527074
x37 = -144.251462677331
x38 = 23.3001455141243
x39 = -24.8709418409192
x40 = -56.2868683768171
x41 = 10.7337748997651
x42 = 48.4328867428426
x43 = -87.7027949127151
x44 = 60.9992573572018
x45 = 44.2440965380563
x46 = 35.8665161284835
x47 = 29.5833308213039
x48 = -89.7971900151083
x49 = -14.3989663289532
x50 = 75.6600230739542
x51 = -31.1541271480988
x52 = 25.3945406165175
x53 = 100.792764302673
x54 = 94.5095789954929
x55 = -12.30457122656
x56 = -96.0803753222878
x57 = -6.02138591938044
x58 = 4.45058959258554
x59 = 31.6777259236971
x60 = 243.21163126541
x61 = -8.11578102177363
x62 = 86.1319985859202
x63 = 63.093652459595
x64 = -52.0980781720307
x65 = -43.720497762458
x66 = 79.8488132787406
x67 = 19.1113553093379
x68 = 67.2824426643814
x68 = 67.2824426643814