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cos(x+pi/4)=0

cos(x+pi/4)=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
   /    pi\    
cos|x + --| = 0
   \    4 /    
$$\cos{\left(x + \frac{\pi}{4} \right)} = 0$$
Solución detallada
Tenemos la ecuación
$$\cos{\left(x + \frac{\pi}{4} \right)} = 0$$
es la ecuación trigonométrica más simple
cambiando el signo de 0

Obtenemos:
$$\cos{\left(x + \frac{\pi}{4} \right)} = 0$$
Esta ecuación se reorganiza en
$$x + \frac{\pi}{4} = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$x + \frac{\pi}{4} = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
O
$$x + \frac{\pi}{4} = \pi n + \frac{\pi}{2}$$
$$x + \frac{\pi}{4} = \pi n - \frac{\pi}{2}$$
, donde n es cualquier número entero
Transportemos
$$\frac{\pi}{4}$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$x = \pi n + \frac{\pi}{4}$$
$$x = \pi n - \frac{3 \pi}{4}$$
Gráfica
Respuesta rápida [src]
     pi
x1 = --
     4 
$$x_{1} = \frac{\pi}{4}$$
     5*pi
x2 = ----
      4  
$$x_{2} = \frac{5 \pi}{4}$$
x2 = 5*pi/4
Suma y producto de raíces [src]
suma
pi   5*pi
-- + ----
4     4  
$$\frac{\pi}{4} + \frac{5 \pi}{4}$$
=
3*pi
----
 2  
$$\frac{3 \pi}{2}$$
producto
pi 5*pi
--*----
4   4  
$$\frac{\pi}{4} \frac{5 \pi}{4}$$
=
    2
5*pi 
-----
  16 
$$\frac{5 \pi^{2}}{16}$$
5*pi^2/16
Respuesta numérica [src]
x1 = 35.3429173528852
x2 = 0.785398163397448
x3 = 1672.11268987317
x4 = 29.0597320457056
x5 = -14.9225651045515
x6 = 95.0331777710912
x7 = 88.7499924639117
x8 = -30.6305283725005
x9 = 85.6083998103219
x10 = -93.4623814442964
x11 = -55.7632696012188
x12 = -43.1968989868597
x13 = 66.7588438887831
x14 = -8.63937979737193
x15 = -5.49778714378214
x16 = -71.4712328691678
x17 = 7.06858347057703
x18 = 22.776546738526
x19 = -46.3384916404494
x20 = -74.6128255227576
x21 = 44.7676953136546
x22 = -49.4800842940392
x23 = 79.3252145031423
x24 = -62.0464549083984
x25 = 73.0420291959627
x26 = -27.4889357189107
x27 = -68.329640215578
x28 = 57.3340659280137
x29 = -96.6039740978861
x30 = -228.550865548657
x31 = 25.9181393921158
x32 = 38.484510006475
x33 = -52.621676947629
x34 = -21.2057504117311
x35 = -84.037603483527
x36 = -24.3473430653209
x37 = -18.0641577581413
x38 = 19.6349540849362
x39 = 98.174770424681
x40 = 91.8915851175014
x41 = -80.8960108299372
x42 = -65.1880475619882
x43 = 69.9004365423729
x44 = -99.7455667514759
x45 = 10.2101761241668
x46 = 13.3517687777566
x47 = -77.7544181763474
x48 = -36.9137136796801
x49 = 32.2013246992954
x50 = -1535.45340944201
x51 = 41.6261026600648
x52 = 60.4756585816035
x53 = 76.1836218495525
x54 = -40.0553063332699
x55 = -87.1791961371168
x56 = -58.9048622548086
x57 = -2.35619449019234
x58 = 82.4668071567321
x59 = 3.92699081698724
x60 = -11.7809724509617
x61 = 54.1924732744239
x62 = 101.316363078271
x63 = 51.0508806208341
x64 = -90.3207887907066
x65 = 63.6172512351933
x66 = -33.7721210260903
x67 = 16.4933614313464
x68 = 47.9092879672443
x68 = 47.9092879672443
Gráfico
cos(x+pi/4)=0 la ecuación