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tan((4*x+pi)/4)=sqrt(3)/3 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
                  ___
   /4*x + pi\   \/ 3 
tan|--------| = -----
   \   4    /     3  
$$\tan{\left(\frac{4 x + \pi}{4} \right)} = \frac{\sqrt{3}}{3}$$
Solución detallada
Tenemos la ecuación
$$\tan{\left(\frac{4 x + \pi}{4} \right)} = \frac{\sqrt{3}}{3}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x + \frac{\pi}{4} = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{3} \right)}$$
O
$$x + \frac{\pi}{4} = \pi n + \frac{\pi}{6}$$
, donde n es cualquier número entero
Transportemos
$$\frac{\pi}{4}$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$x = \pi n - \frac{\pi}{12}$$
Gráfica
Suma y producto de raíces [src]
suma
-pi 
----
 12 
$$- \frac{\pi}{12}$$
=
-pi 
----
 12 
$$- \frac{\pi}{12}$$
producto
-pi 
----
 12 
$$- \frac{\pi}{12}$$
=
-pi 
----
 12 
$$- \frac{\pi}{12}$$
-pi/12
Respuesta rápida [src]
     -pi 
x1 = ----
      12 
$$x_{1} = - \frac{\pi}{12}$$
x1 = -pi/12
Respuesta numérica [src]
x1 = 56.2868683768171
x2 = 34.2957198016886
x3 = -66.2352451131848
x4 = 90.8443875663049
x5 = 71.9948316447661
x6 = 21.7293491873294
x7 = 31.1541271480988
x8 = 81.4196096055355
x9 = -78.801615727544
x10 = 46.8620904160477
x11 = -25.3945406165175
x12 = 75.1364242983559
x13 = -3.40339204138894
x14 = 28.012534494509
x15 = 18.5877565337396
x16 = -91.3679863419031
x17 = 12.30457122656
x18 = 100.269165527074
x19 = -34.8193185772869
x20 = -100.792764302673
x21 = 15.4461638801498
x22 = 50.0036830696375
x23 = -41.1025038844665
x24 = -56.8104671524154
x25 = -69.3768377667746
x26 = 87.7027949127151
x27 = -19.1113553093379
x28 = -47.3856891916461
x29 = 53.1452757232273
x30 = 97.1275728734844
x31 = -94.5095789954929
x32 = -22.2529479629277
x33 = 2.87979326579064
x34 = -15.9697626557481
x35 = -44.2440965380563
x36 = -88.2263936883134
x37 = 59.4284610304069
x38 = 6.02138591938044
x39 = -75.6600230739542
x40 = 24.8709418409192
x41 = -53.6688744988256
x42 = -59.9520598060052
x43 = -37.9609112308767
x44 = -12.8281700021583
x45 = -0.261799387799149
x46 = -28.5361332701073
x47 = -9.68657734856853
x48 = 84.5612022591253
x49 = -50.5272818452358
x50 = 40.5789051088682
x51 = 43.720497762458
x52 = 68.8532389911763
x53 = 37.4373124552784
x54 = -85.0848010347236
x55 = 78.2780169519457
x56 = 62.5700536839967
x57 = -6.54498469497874
x58 = 65.7116463375865
x59 = -81.9432083811338
x60 = -31.6777259236971
x61 = 9.16297857297023
x62 = 93.9859802198946
x63 = -63.093652459595
x64 = -97.6511716490827
x65 = -72.5184304203644
x65 = -72.5184304203644