Sr Examen

sinx=cosx la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
sin(x) = cos(x)
$$\sin{\left(x \right)} = \cos{\left(x \right)}$$
Solución detallada
Tenemos la ecuación
$$\sin{\left(x \right)} = \cos{\left(x \right)}$$
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
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 rápida [src]
     pi
x1 = --
     4 
$$x_{1} = \frac{\pi}{4}$$
x1 = pi/4
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 = 41.6261026600648
x51 = 60.4756585816035
x52 = 76.1836218495525
x53 = -40.0553063332699
x54 = -87.1791961371168
x55 = -58.9048622548086
x56 = -2.35619449019234
x57 = 82.4668071567321
x58 = 3.92699081698724
x59 = -11.7809724509617
x60 = 54.1924732744239
x61 = 101.316363078271
x62 = 51.0508806208341
x63 = -90.3207887907066
x64 = 63.6172512351933
x65 = -33.7721210260903
x66 = 16.4933614313464
x67 = 47.9092879672443
x67 = 47.9092879672443
Gráfico
sinx=cosx la ecuación