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sin^2(9x) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   2         
sin (9*x) = 0
sin⁡2(9x)=0\sin^{2}{\left(9 x \right)} = 0
Simplificar
Solución detallada
Tenemos la ecuación
sin⁡2(9x)=0\sin^{2}{\left(9 x \right)} = 0
cambiamos
sin⁡2(9x)=0\sin^{2}{\left(9 x \right)} = 0
sin⁡2(9x)=0\sin^{2}{\left(9 x \right)} = 0
Sustituimos
w=sin⁡(9x)w = \sin{\left(9 x \right)}
Es la ecuación de la forma
a*w^2 + b*w + c = 0

La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
w1=D−b2aw_{1} = \frac{\sqrt{D} - b}{2 a}
w2=−D−b2aw_{2} = \frac{- \sqrt{D} - b}{2 a}
donde D = b^2 - 4*a*c es el discriminante.
Como
a=1a = 1
b=0b = 0
c=0c = 0
, entonces
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (1) * (0) = 0

Como D = 0 hay sólo una raíz.
w = -b/2a = -0/2/(1)

w1=0w_{1} = 0
hacemos cambio inverso
sin⁡(9x)=w\sin{\left(9 x \right)} = w
Tenemos la ecuación
sin⁡(9x)=w\sin{\left(9 x \right)} = w
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
9x=2πn+asin⁡(w)9 x = 2 \pi n + \operatorname{asin}{\left(w \right)}
9x=2πn−asin⁡(w)+π9 x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi
O
9x=2πn+asin⁡(w)9 x = 2 \pi n + \operatorname{asin}{\left(w \right)}
9x=2πn−asin⁡(w)+π9 x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
99
sustituimos w:
x1=2πn9+asin⁡(w1)9x_{1} = \frac{2 \pi n}{9} + \frac{\operatorname{asin}{\left(w_{1} \right)}}{9}
x1=2πn9+asin⁡(0)9x_{1} = \frac{2 \pi n}{9} + \frac{\operatorname{asin}{\left(0 \right)}}{9}
x1=2πn9x_{1} = \frac{2 \pi n}{9}
x2=2πn9−asin⁡(w1)9+π9x_{2} = \frac{2 \pi n}{9} - \frac{\operatorname{asin}{\left(w_{1} \right)}}{9} + \frac{\pi}{9}
x2=2πn9−asin⁡(0)9+π9x_{2} = \frac{2 \pi n}{9} - \frac{\operatorname{asin}{\left(0 \right)}}{9} + \frac{\pi}{9}
x2=2πn9+π9x_{2} = \frac{2 \pi n}{9} + \frac{\pi}{9}
Gráfica
0-80-60-40-2020406080-10010002
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
x1 = 0
x1=0x_{1} = 0 
     pi
x2 = --
     9
x2=π9x_{2} = \frac{\pi}{9} 
x2 = pi/9
Suma y producto de raíces [src] 
suma
pi
--
9
π9\frac{\pi}{9} 
=
pi
--
9
π9\frac{\pi}{9} 
producto
  pi
0*--
  9
0π90 \frac{\pi}{9} 
=
0
00 
0
Respuesta numérica [src] 
x1 = 50.265482452683
x2 = 78.1907505288855
x3 = 100.181899072028
x4 = -82.0304748661836
x5 = 59.6902604086997
x6 = 72.2566310284747
x7 = 64.2281164938319
x8 = 86.2192650777605
x9 = 42.2369679097976
x10 = -57.5958653134514
x11 = -53.7561409563741
x12 = -36.3028484193336
x13 = -30.0196631340415
x14 = 82.0304747803675
x15 = 8.0285144916442
x16 = 0.0
x17 = 56.1996019568152
x18 = -74.3510261362399
x19 = -103.672557606959
x20 = 20.2458193264786
x21 = -43.6332313053393
x22 = -65.9734457917016
x23 = 326.376570109802
x24 = -1.74532925507657
x25 = -52.0108117033594
x26 = 94.2477796094142
x27 = -153.938040058112
x28 = 95.9931088650419
x29 = 91.4552527164453
x30 = 30.0196630866935
x31 = -29.3215315149923
x32 = 28.2743338989553
x33 = -43.9822971915037
x34 = -45.7276263952845
x35 = 74.0019602819512
x36 = -8.02851461069728
x37 = -17.8023583275558
x38 = 52.0108116886708
x39 = 29.6705972731859
x40 = -61.7846554877323
x41 = -69.8131700470521
x42 = 26.1799387598344
x43 = 43.982297153311
x44 = -75.7472895384448
x45 = -74.0019602824506
x46 = 12.2173047950457
x47 = -83.775804071326
x48 = 1619.31648001743
x49 = 34.2084533774898
x50 = -23.7364778325298
x51 = 21.9911485810311
x52 = 53.4070750870823
x53 = -47.8220215831374
x54 = -31.7649923728221
x55 = -91.8043186123259
x56 = -3.49065846416499
x57 = -21.9911485909836
x58 = -39.7935069057831
x59 = 4.18879024162074
x60 = 23.7364778260274
x61 = -9.77384378874014
x62 = -77.492618774742
x63 = 70.5113017801434
x64 = 97.7384381153428
x65 = -95.9931088711301
x66 = -97.7384381171806
x67 = 65.9734456929592
x67 = 65.9734456929592
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