Sr Examen

cosx=-sinx la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
cos(x) = -sin(x)
$$\cos{\left(x \right)} = - \sin{\left(x \right)}$$
Solución detallada
Tenemos la ecuación
$$\cos{\left(x \right)} = - \sin{\left(x \right)}$$
cambiamos:
$$\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} = -1$$
o
$$\tan{\left(x \right)} = -1$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{atan}{\left(1 \right)}$$
O
$$x = \pi n + \frac{\pi}{4}$$
, donde n es cualquier número entero
Gráfica
Respuesta rápida [src]
     -pi 
x1 = ----
      4  
$$x_{1} = - \frac{\pi}{4}$$
x1 = -pi/4
Suma y producto de raíces [src]
suma
-pi 
----
 4  
$$- \frac{\pi}{4}$$
=
-pi 
----
 4  
$$- \frac{\pi}{4}$$
producto
-pi 
----
 4  
$$- \frac{\pi}{4}$$
=
-pi 
----
 4  
$$- \frac{\pi}{4}$$
-pi/4
Respuesta numérica [src]
x1 = -88.7499924639117
x2 = 58.9048622548086
x3 = 351.072979038659
x4 = 93.4623814442964
x5 = 30.6305283725005
x6 = -66.7588438887831
x7 = 55.7632696012188
x8 = -16.4933614313464
x9 = 40.0553063332699
x10 = -47.9092879672443
x11 = -25.9181393921158
x12 = 46.3384916404494
x13 = 71.4712328691678
x14 = 33.7721210260903
x15 = 49.4800842940392
x16 = 36.9137136796801
x17 = 90.3207887907066
x18 = -76.1836218495525
x19 = -22.776546738526
x20 = -29.0597320457056
x21 = 2.35619449019234
x22 = -73.0420291959627
x23 = 99.7455667514759
x24 = 80.8960108299372
x25 = -98.174770424681
x26 = -10.2101761241668
x27 = 96.6039740978861
x28 = 74.6128255227576
x29 = 62.0464549083984
x30 = -7.06858347057703
x31 = 14.9225651045515
x32 = -57.3340659280137
x33 = -0.785398163397448
x34 = -85.6083998103219
x35 = -107.59954838545
x36 = 43.1968989868597
x37 = 65.1880475619882
x38 = 8.63937979737193
x39 = -79.3252145031423
x40 = -69.9004365423729
x41 = -51.0508806208341
x42 = 68.329640215578
x43 = 18.0641577581413
x44 = 87.1791961371168
x45 = -95.0331777710912
x46 = 52.621676947629
x47 = -63.6172512351933
x48 = 5.49778714378214
x49 = -82.4668071567321
x50 = 11.7809724509617
x51 = -19.6349540849362
x52 = 84.037603483527
x53 = -54.1924732744239
x54 = 21.2057504117311
x55 = -91.8915851175014
x56 = -44.7676953136546
x57 = 24.3473430653209
x58 = -32.2013246992954
x59 = -41.6261026600648
x60 = -60.4756585816035
x61 = 27.4889357189107
x62 = -13.3517687777566
x63 = -35.3429173528852
x64 = 77.7544181763474
x65 = -3.92699081698724
x66 = -38.484510006475
x66 = -38.484510006475