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2*sinx-3*cosx=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
2*sin(x) - 3*cos(x) = 0
$$2 \sin{\left(x \right)} - 3 \cos{\left(x \right)} = 0$$
Solución detallada
Tenemos la ecuación
$$2 \sin{\left(x \right)} - 3 \cos{\left(x \right)} = 0$$
cambiamos:
$$\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}} = 3$$
o
$$2 \tan{\left(x \right)} = 3$$
es la ecuación trigonométrica más simple
Dividamos ambos miembros de la ecuación en 2

La ecuación se convierte en
$$\tan{\left(x \right)} = - \frac{3}{2}$$
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{atan}{\left(- \frac{3}{2} \right)}$$
O
$$x = \pi n - \operatorname{atan}{\left(\frac{3}{2} \right)}$$
, donde n es cualquier número entero
Gráfica
Respuesta rápida [src]
x1 = atan(3/2)
$$x_{1} = \operatorname{atan}{\left(\frac{3}{2} \right)}$$
x1 = atan(3/2)
Suma y producto de raíces [src]
suma
atan(3/2)
$$\operatorname{atan}{\left(\frac{3}{2} \right)}$$
=
atan(3/2)
$$\operatorname{atan}{\left(\frac{3}{2} \right)}$$
producto
atan(3/2)
$$\operatorname{atan}{\left(\frac{3}{2} \right)}$$
=
atan(3/2)
$$\operatorname{atan}{\left(\frac{3}{2} \right)}$$
atan(3/2)
Respuesta numérica [src]
x1 = -93.2649858844465
x2 = 1172.79685351224
x3 = -5.30039158393226
x4 = -96.4065785380363
x5 = -86.9818005772669
x6 = -2.15879893034246
x7 = 22.9739422983759
x8 = 95.2305733309411
x9 = 66.956239448633
x10 = -46.1410960805996
x11 = -17.8667621982914
x12 = -83.8402079236771
x13 = -14.7251695447016
x14 = -52.4242813877792
x15 = 85.8057953701718
x16 = -61.8490593485485
x17 = -33.5747254662404
x18 = 7.26597903042692
x19 = 4.12438637683712
x20 = 63.8146467950432
x21 = -1959.37102211678
x22 = 57.5314614878636
x23 = 29.2571276055555
x24 = -30.4331328126506
x25 = 38.6819055663249
x26 = 76.3810174094024
x27 = 32.3987202591453
x28 = -64.9906520021383
x29 = -99.5481711916261
x30 = 619.876546480437
x31 = -71.2738373093179
x32 = 44.9650908735044
x33 = 224.035872128123
x34 = -49.2826887341894
x35 = -77.5570226164975
x36 = 123.504907213249
x37 = 13.5491643376065
x38 = 26.1155349519657
x39 = 51.248276180684
x40 = 54.3898688342738
x41 = -8.44198423752205
x42 = 0.982793723247329
x43 = -80.6986152700873
x44 = 82.664202716582
x45 = -68.1322446557281
x46 = 79.5226100629922
x47 = 19.8323496447861
x48 = -11.5835768911118
x49 = -118.397727113165
x50 = 92.0889806773513
x51 = 16.6907569911963
x52 = -24.149947505471
x53 = -27.2915401590608
x54 = -42.9995034270098
x55 = -55.565874041369
x56 = 35.5403129127351
x57 = 88.9473880237615
x58 = 10.4075716840167
x59 = -74.4154299629077
x60 = 70.0978321022228
x61 = 41.8234982199146
x62 = -90.1233932308567
x63 = 60.6730541414534
x64 = -39.85791077342
x65 = 98.3721659845309
x66 = 48.1066835270942
x67 = -21.0083548518812
x68 = -58.7074666949587
x69 = 73.2394247558126
x70 = -36.7163181198302
x70 = -36.7163181198302