Sr Examen

Otras calculadoras

3tg(x)=2cos(x) la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
3*tan(x) = 2*cos(x)
$$3 \tan{\left(x \right)} = 2 \cos{\left(x \right)}$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
pi   5*pi     pi        /      ___\     pi        /      ___\
-- + ---- + - -- - I*log\2 - \/ 3 / + - -- - I*log\2 + \/ 3 /
6     6       2                         2
$$\left(- \frac{\pi}{2} - i \log{\left(\sqrt{3} + 2 \right)}\right) + \left(\left(\frac{\pi}{6} + \frac{5 \pi}{6}\right) + \left(- \frac{\pi}{2} - i \log{\left(2 - \sqrt{3} \right)}\right)\right)$$ 
=
       /      ___\        /      ___\
- I*log\2 + \/ 3 / - I*log\2 - \/ 3 /
$$- i \log{\left(\sqrt{3} + 2 \right)} - i \log{\left(2 - \sqrt{3} \right)}$$ 
producto
pi 5*pi /  pi        /      ___\\ /  pi        /      ___\\
--*----*|- -- - I*log\2 - \/ 3 /|*|- -- - I*log\2 + \/ 3 /|
6   6   \  2                    / \  2                    /
$$\frac{\pi}{6} \frac{5 \pi}{6} \left(- \frac{\pi}{2} - i \log{\left(2 - \sqrt{3} \right)}\right) \left(- \frac{\pi}{2} - i \log{\left(\sqrt{3} + 2 \right)}\right)$$ 
=
    2 /            /      ___\\ /            /      ___\\
5*pi *\pi + 2*I*log\2 + \/ 3 //*\pi + 2*I*log\2 - \/ 3 //
---------------------------------------------------------
                           144
$$\frac{5 \pi^{2} \left(\pi + 2 i \log{\left(2 - \sqrt{3} \right)}\right) \left(\pi + 2 i \log{\left(\sqrt{3} + 2 \right)}\right)}{144}$$ 
5*pi^2*(pi + 2*i*log(2 + sqrt(3)))*(pi + 2*i*log(2 - sqrt(3)))/144
Respuesta rápida [src] 
     pi
x1 = --
     6
$$x_{1} = \frac{\pi}{6}$$ 
     5*pi
x2 = ----
      6
$$x_{2} = \frac{5 \pi}{6}$$ 
       pi        /      ___\
x3 = - -- - I*log\2 - \/ 3 /
       2
$$x_{3} = - \frac{\pi}{2} - i \log{\left(2 - \sqrt{3} \right)}$$ 
       pi        /      ___\
x4 = - -- - I*log\2 + \/ 3 /
       2
$$x_{4} = - \frac{\pi}{2} - i \log{\left(\sqrt{3} + 2 \right)}$$ 
x4 = -pi/2 - i*log(sqrt(3) + 2)
Respuesta numérica [src] 
x1 = 82.2050077689329
x2 = -60.2138591938044
x3 = -79.0634151153431
x4 = 2.61799387799149
x5 = -30.8923277602996
x6 = 38.2227106186758
x7 = 101.054563690472
x8 = -72.7802298081635
x9 = -68.5914396033772
x10 = 6.80678408277789
x11 = -43.4586983746588
x12 = -87.4409955249159
x13 = 59.1666616426078
x14 = -91.6297857297023
x15 = 15.1843644923507
x16 = 34.0339204138894
x17 = 88.4881930761125
x18 = 40.317105721069
x19 = -97.9129710368819
x20 = -62.3082542961976
x21 = 44.5058959258554
x22 = -18.3259571459405
x23 = -35.081117965086
x24 = -53.9306738866248
x25 = 50.789081233035
x26 = -28.7979326579064
x27 = 57.0722665402146
x28 = 27.7507351067098
x29 = -22.5147473507269
x30 = 21.4675497995303
x31 = -12.0427718387609
x32 = 31.9395253114962
x33 = -3.66519142918809
x34 = 8.90117918517108
x35 = 96.8657734856853
x36 = 0.523598775598299
x37 = -56.025068989018
x38 = -74.8746249105567
x39 = 84.2994028713261
x40 = 78.0162175641465
x41 = 65.4498469497874
x42 = -49.7418836818384
x43 = -24.60914245312
x44 = -16.2315620435473
x45 = -93.7241808320955
x46 = 25.6563400043166
x47 = -66.497044500984
x48 = 94.7713783832921
x49 = 46.6002910282486
x50 = 63.3554518473942
x51 = -85.3466004225227
x52 = -9.94837673636768
x53 = -41.3643032722656
x54 = 13.0899693899575
x55 = 52.8834763354282
x56 = 75.9218224617533
x57 = -100.007366139275
x58 = -37.1755130674792
x59 = -47.6474885794452
x60 = 69.6386371545737
x61 = -81.1578102177363
x62 = -5.75958653158129
x63 = 71.733032256967
x64 = 90.5825881785057
x65 = 19.3731546971371
x65 = 19.3731546971371
    © Sr Examen