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tan(x-3*pi/4)=-sqrt(3) la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
   /    3*pi\      ___
tan|x - ----| = -\/ 3 
   \     4  /         
$$\tan{\left(x - \frac{3 \pi}{4} \right)} = - \sqrt{3}$$
Solución detallada
Tenemos la ecuación
$$\tan{\left(x - \frac{3 \pi}{4} \right)} = - \sqrt{3}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x + \frac{\pi}{4} = \pi n + \operatorname{atan}{\left(- \sqrt{3} \right)}$$
O
$$x + \frac{\pi}{4} = \pi n - \frac{\pi}{3}$$
, donde n es cualquier número entero
Transportemos
$$\frac{\pi}{4}$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$x = \pi n - \frac{7 \pi}{12}$$
Gráfica
Respuesta rápida [src]
     -7*pi
x1 = -----
       12 
$$x_{1} = - \frac{7 \pi}{12}$$
x1 = -7*pi/12
Suma y producto de raíces [src]
suma
-7*pi
-----
  12 
$$- \frac{7 \pi}{12}$$
=
-7*pi
-----
  12 
$$- \frac{7 \pi}{12}$$
producto
-7*pi
-----
  12 
$$- \frac{7 \pi}{12}$$
=
-7*pi
-----
  12 
$$- \frac{7 \pi}{12}$$
-7*pi/12
Respuesta numérica [src]
x1 = 26.4417381677141
x2 = 89.27359123951
x3 = -55.2396708256205
x4 = -33.248522250492
x5 = 42.1497014356631
x6 = -30.1069295969022
x7 = 45.2912940892529
x8 = -11.2573736753634
x9 = -61.5228561328001
x10 = -1.83259571459405
x11 = 7.59218224617533
x12 = -67.8060414399797
x13 = 48.4328867428426
x14 = 86.1319985859202
x15 = 67.2824426643814
x16 = -83.5140047079287
x17 = 10.7337748997651
x18 = 4.45058959258554
x19 = -77.2308194007491
x20 = -99.2219679758776
x21 = -14.3989663289532
x22 = -52.0980781720307
x23 = 23.3001455141243
x24 = 76.7072206251508
x25 = -58.3812634792103
x26 = -39.5317075576716
x27 = -36.3901149040818
x28 = 57.857664703612
x29 = -17.540558982543
x30 = 1.30899693899575
x31 = 20.1585528605345
x32 = 29.5833308213039
x33 = 51.5744793964324
x34 = -20.6821516361328
x35 = -80.3724120543389
x36 = -92.9387826686981
x37 = 92.4151838930998
x38 = 54.7160720500222
x39 = 73.565627971561
x40 = 13.8753675533549
x41 = 64.1408500107916
x42 = -42.6733002112614
x43 = -89.7971900151083
x44 = 35.8665161284835
x45 = 32.7249234748937
x46 = 95.5567765466895
x47 = -48.9564855184409
x48 = -86.6555973615185
x49 = -96.0803753222878
x50 = -45.8148928648512
x51 = -23.8237442897226
x52 = -102.363560629467
x53 = 79.8488132787406
x54 = 101.839961853869
x55 = 70.4240353179712
x56 = -74.0892267471593
x57 = -64.6644487863899
x58 = -70.9476340935695
x59 = -8.11578102177363
x59 = -8.11578102177363