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cos(x+(pi/6))=sqrt(2)/2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
                ___
   /    pi\   \/ 2 
cos|x + --| = -----
   \    6 /     2  
$$\cos{\left(x + \frac{\pi}{6} \right)} = \frac{\sqrt{2}}{2}$$
Solución detallada
Tenemos la ecuación
$$\cos{\left(x + \frac{\pi}{6} \right)} = \frac{\sqrt{2}}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x + \frac{\pi}{6} = \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$x + \frac{\pi}{6} = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
O
$$x + \frac{\pi}{6} = \pi n + \frac{\pi}{4}$$
$$x + \frac{\pi}{6} = \pi n - \frac{3 \pi}{4}$$
, donde n es cualquier número entero
Transportemos
$$\frac{\pi}{6}$$
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
Respuesta rápida [src]
     pi
x1 = --
     12
$$x_{1} = \frac{\pi}{12}$$
     19*pi
x2 = -----
       12 
$$x_{2} = \frac{19 \pi}{12}$$
x2 = 19*pi/12
Suma y producto de raíces [src]
suma
pi   19*pi
-- + -----
12     12 
$$\frac{\pi}{12} + \frac{19 \pi}{12}$$
=
5*pi
----
 3  
$$\frac{5 \pi}{3}$$
producto
pi 19*pi
--*-----
12   12 
$$\frac{\pi}{12} \frac{19 \pi}{12}$$
=
     2
19*pi 
------
 144  
$$\frac{19 \pi^{2}}{144}$$
19*pi^2/144
Respuesta numérica [src]
x1 = 61.5228561328001
x2 = -31.1541271480988
x3 = -95.5567765466895
x4 = -76.7072206251508
x5 = -12.30457122656
x6 = -68.8532389911763
x7 = 42.6733002112614
x8 = -6.02138591938044
x9 = -57.857664703612
x10 = 17.540558982543
x11 = -51.5744793964324
x12 = -82.9904059323304
x13 = 6.54498469497874
x14 = 31.6777259236971
x15 = -126.972703082587
x16 = 81.9432083811338
x17 = -64.1408500107916
x18 = 80.3724120543389
x19 = -1.30899693899575
x20 = -50.0036830696375
x21 = -13.8753675533549
x22 = 19.1113553093379
x23 = 48.9564855184409
x24 = 63.093652459595
x25 = -93.9859802198946
x26 = 74.0892267471593
x27 = 30.1069295969022
x28 = -43.720497762458
x29 = -75.1364242983559
x30 = 88.2263936883134
x31 = -32.7249234748937
x32 = 12.8281700021583
x33 = -1634.93717680569
x34 = 55.2396708256205
x35 = 44.2440965380563
x36 = -100.269165527074
x37 = -37.4373124552784
x38 = -81.4196096055355
x39 = -89.27359123951
x40 = -39.0081087820733
x41 = -45.2912940892529
x42 = 100.792764302673
x43 = -70.4240353179712
x44 = -244.782427592205
x45 = 37.9609112308767
x46 = -56.2868683768171
x47 = -87.7027949127151
x48 = -20.1585528605345
x49 = 99.2219679758776
x50 = 69.3768377667746
x51 = -7.59218224617533
x52 = -18.5877565337396
x53 = 11.2573736753634
x54 = 0.261799387799149
x55 = 75.6600230739542
x56 = 92.9387826686981
x57 = 4.97418836818384
x58 = -62.5700536839967
x59 = 23.8237442897226
x60 = 56.8104671524154
x61 = 136.921079818955
x62 = 36.3901149040818
x63 = 50.5272818452358
x64 = 67.8060414399797
x65 = 94.5095789954929
x66 = -26.4417381677141
x67 = 86.6555973615185
x68 = 25.3945406165175
x69 = -24.8709418409192
x69 = -24.8709418409192