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cosx/1+2sinx la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
cos(x)               
------ + 2*sin(x) = 0
  1                  
$$2 \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{1} = 0$$
Solución detallada
Tenemos la ecuación
$$2 \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{1} = 0$$
cambiamos:
$$\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}} = -1$$
o
$$2 \tan{\left(x \right)} = -1$$
es la ecuación trigonométrica más simple
Dividamos ambos miembros de la ecuación en 2

La ecuación se convierte en
$$\tan{\left(x \right)} = \frac{1}{2}$$
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{atan}{\left(\frac{1}{2} \right)}$$
O
$$x = \pi n + \operatorname{atan}{\left(\frac{1}{2} \right)}$$
, donde n es cualquier número entero
Gráfica
Respuesta rápida [src]
x1 = -atan(1/2)
$$x_{1} = - \operatorname{atan}{\left(\frac{1}{2} \right)}$$
x1 = -atan(1/2)
Suma y producto de raíces [src]
suma
-atan(1/2)
$$- \operatorname{atan}{\left(\frac{1}{2} \right)}$$
=
-atan(1/2)
$$- \operatorname{atan}{\left(\frac{1}{2} \right)}$$
producto
-atan(1/2)
$$- \operatorname{atan}{\left(\frac{1}{2} \right)}$$
=
-atan(1/2)
$$- \operatorname{atan}{\left(\frac{1}{2} \right)}$$
-atan(1/2)
Respuesta numérica [src]
x1 = -3.6052402625906
x2 = 27.8106862733073
x3 = 68.6513907699746
x4 = -44.4459447592579
x5 = -35.0211667984885
x6 = 34.0938715804869
x7 = -50.7291300664375
x8 = 15.2443156589482
x9 = 8.96113035176857
x10 = 81.2177613843338
x11 = -41.3043521056681
x12 = 96.9257246522828
x13 = 5.81953769817878
x14 = -31.8795741448987
x15 = 52.9434275020257
x16 = -19.3132035305396
x17 = -75.8618712951559
x18 = 46.6602421948461
x19 = -53.8707227200273
x20 = -100.994612523874
x21 = -97.8530198702844
x22 = 100.067317305873
x23 = 93.784131998693
x24 = 30.9522789268971
x25 = 59.2266128092053
x26 = 71.7929834235644
x27 = -82.1450566023354
x28 = -94.7114272166946
x29 = 12.1027230053584
x30 = 191.173504259977
x31 = 18.385908312538
x32 = 56.0850201556155
x33 = 74.9345760771542
x34 = -6.74683291618039
x35 = -66.4370933343865
x36 = 65.5097981163849
x37 = 37.2354642340767
x38 = -25.5963888377192
x39 = -16.1716108769498
x40 = 21.5275009661277
x41 = 84.3593540379236
x42 = -13.03001822336
x43 = -72.7202786415661
x44 = -57.0123153736171
x45 = -286.348579085672
x46 = -63.2955006807967
x47 = -60.1539080272069
x48 = 90.6425393451032
x49 = 40.3770568876665
x50 = -85.2866492559252
x51 = 62.3682054627951
x52 = -88.428241909515
x53 = 24.6690936197175
x54 = -47.5875374128477
x55 = 835.199998245884
x56 = -79.0034639487456
x57 = -38.1627594520783
x58 = -22.4547961841294
x59 = 49.8018348484359
x60 = 87.5009466915134
x61 = -69.5786859879763
x62 = 78.076168730744
x63 = -141.835317020542
x64 = -91.5698345631048
x65 = 2.67794504458899
x66 = -0.463647609000806
x67 = -28.7379814913089
x68 = -9.88842556977019
x69 = 43.5186495412563
x69 = 43.5186495412563