Sr Examen

Otras calculadoras

sin(pi-x)+cos(3*pi/2+x)+2*(sin(x))^2=3/2 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*pi    \        2         
sin(pi - x) + cos|---- + x| + 2*sin (x) = 3/2
                 \ 2      /                  
$$\left(\sin{\left(\pi - x \right)} + \cos{\left(x + \frac{3 \pi}{2} \right)}\right) + 2 \sin^{2}{\left(x \right)} = \frac{3}{2}$$
Gráfica
Respuesta rápida [src]
     pi
x1 = --
     6 
$$x_{1} = \frac{\pi}{6}$$
     5*pi
x2 = ----
      6  
$$x_{2} = \frac{5 \pi}{6}$$
x3 = pi + I*im(asin(3/2)) + re(asin(3/2))
$$x_{3} = \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}$$
x4 = -re(asin(3/2)) - I*im(asin(3/2))
$$x_{4} = - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}$$
x4 = -re(asin(3/2)) - i*im(asin(3/2))
Suma y producto de raíces [src]
suma
pi   5*pi                                                                          
-- + ---- + pi + I*im(asin(3/2)) + re(asin(3/2)) + -re(asin(3/2)) - I*im(asin(3/2))
6     6                                                                            
$$\left(\left(\frac{\pi}{6} + \frac{5 \pi}{6}\right) + \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right)\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right)$$
=
2*pi
$$2 \pi$$
producto
pi 5*pi                                                                          
--*----*(pi + I*im(asin(3/2)) + re(asin(3/2)))*(-re(asin(3/2)) - I*im(asin(3/2)))
6   6                                                                            
$$\frac{\pi}{6} \frac{5 \pi}{6} \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right)$$
=
     2                                                                         
-5*pi *(I*im(asin(3/2)) + re(asin(3/2)))*(pi + I*im(asin(3/2)) + re(asin(3/2)))
-------------------------------------------------------------------------------
                                       36                                      
$$- \frac{5 \pi^{2} \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right)}{36}$$
-5*pi^2*(i*im(asin(3/2)) + re(asin(3/2)))*(pi + i*im(asin(3/2)) + re(asin(3/2)))/36
Respuesta numérica [src]
x1 = -47.6474885794452
x2 = 21.4675497995303
x3 = -93.7241808320955
x4 = 69.6386371545737
x5 = 52.8834763354282
x6 = -79.0634151153431
x7 = -66.497044500984
x8 = -72.7802298081635
x9 = 15.1843644923507
x10 = 57.0722665402146
x11 = -24.60914245312
x12 = 101.054563690472
x13 = 84.2994028713261
x14 = 63.3554518473942
x15 = 90.5825881785057
x16 = 78.0162175641465
x17 = 2.61799387799149
x18 = -41.3643032722656
x19 = -43.4586983746588
x20 = -37.1755130674792
x21 = -22.5147473507269
x22 = 0.523598775598299
x23 = 96.8657734856853
x24 = 38.2227106186758
x25 = -68.5914396033772
x26 = 44.5058959258554
x27 = -60.2138591938044
x28 = 94.7713783832921
x29 = -53.9306738866248
x30 = 245.567825755602
x31 = 50.789081233035
x32 = 27.7507351067098
x33 = -5.75958653158129
x34 = -87.4409955249159
x35 = 65.4498469497874
x36 = -16.2315620435473
x37 = -56.025068989018
x38 = 19.3731546971371
x39 = 13.0899693899575
x40 = -9.94837673636768
x41 = -12.0427718387609
x42 = -3.66519142918809
x43 = 6.80678408277789
x44 = -81.1578102177363
x45 = -97.9129710368819
x46 = -28.7979326579064
x47 = 88.4881930761125
x48 = -18.3259571459405
x49 = 31.9395253114962
x50 = 46.6002910282486
x51 = 40.317105721069
x52 = 82.2050077689329
x53 = 59.1666616426078
x54 = 8.90117918517108
x55 = 75.9218224617533
x56 = -91.6297857297023
x57 = 34.0339204138894
x58 = 71.733032256967
x59 = -85.3466004225227
x60 = -100.007366139275
x61 = -62.3082542961976
x62 = -49.7418836818384
x63 = 25.6563400043166
x64 = -35.081117965086
x64 = -35.081117965086