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sin(x)^2=0

sin(x)^2=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
   2       
sin (x) = 0
sin2(x)=0\sin^{2}{\left(x \right)} = 0
Solución detallada
Tenemos la ecuación
sin2(x)=0\sin^{2}{\left(x \right)} = 0
cambiamos
sin2(x)=0\sin^{2}{\left(x \right)} = 0
sin2(x)=0\sin^{2}{\left(x \right)} = 0
Sustituimos
w=sin(x)w = \sin{\left(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=Db2aw_{1} = \frac{\sqrt{D} - b}{2 a}
w2=Db2aw_{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(x)=w\sin{\left(x \right)} = w
Tenemos la ecuación
sin(x)=w\sin{\left(x \right)} = w
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
x=2πn+asin(w)x = 2 \pi n + \operatorname{asin}{\left(w \right)}
x=2πnasin(w)+πx = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi
O
x=2πn+asin(w)x = 2 \pi n + \operatorname{asin}{\left(w \right)}
x=2πnasin(w)+πx = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi
, donde n es cualquier número entero
sustituimos w:
x1=2πn+asin(w1)x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}
x1=2πn+asin(0)x_{1} = 2 \pi n + \operatorname{asin}{\left(0 \right)}
x1=2πnx_{1} = 2 \pi n
x2=2πnasin(w1)+πx_{2} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi
x2=2πnasin(0)+πx_{2} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi
x2=2πn+πx_{2} = 2 \pi n + \pi
Gráfica
0-80-60-40-2020406080-10010002
Suma y producto de raíces [src]
suma
pi
π\pi
=
pi
π\pi
producto
0*pi
0π0 \pi
=
0
00
0
Respuesta rápida [src]
x1 = 0
x1=0x_{1} = 0
x2 = pi
x2=πx_{2} = \pi
x2 = pi
Respuesta numérica [src]
x1 = -47.123890151099
x2 = -37.6991118771514
x3 = 91.1061867314459
x4 = 84.8230010166547
x5 = -9.42477812668337
x6 = -69.1150386253436
x7 = -56.5486675191652
x8 = 97.3893725148693
x9 = -6.28318513794069
x10 = -91.1061872003049
x11 = -62.8318528379059
x12 = -47.1238900492539
x13 = -34.5575189426108
x14 = 40.8407042560881
x15 = 37.6991120192083
x16 = 31.4159267865366
x17 = -97.3893724403711
x18 = 50.2654824463473
x19 = -18.8495556944209
x20 = -94.2477794529919
x21 = 75.3982241944528
x22 = 69.1150381602162
x23 = -1734.15914475848
x24 = 97.3893727097471
x25 = -87.9645943587732
x26 = 91.1061871583643
x27 = 31.4159271479423
x28 = -62.8318532583801
x29 = -100.530964672522
x30 = -75.3982238620294
x31 = 72.256631027719
x32 = 9.42477821024198
x33 = 75.3982239388525
x34 = 0.0
x35 = 69.1150385885879
x36 = -31.4159267959754
x37 = -65.9734457650176
x38 = -28.2743337166085
x39 = 3.14159287686128
x40 = -12.5663703661411
x41 = -72.2566308741333
x42 = -18.8495561207399
x43 = 62.8318528326557
x44 = -15.7079632965264
x45 = 94.2477796093525
x46 = 53.4070756765307
x47 = -84.8230018263493
x48 = 6.28318528425126
x49 = -106.814150357553
x50 = 34.5575190304759
x51 = 40.840703919946
x52 = -3.14159289677385
x53 = -25.132741473063
x54 = -78.5398160958028
x55 = 56.5486676091327
x56 = 47.123889589354
x57 = -84.82300141007
x58 = -43.9822971745789
x59 = 25.1327414478072
x60 = 18.8495554002244
x61 = -53.4070752836338
x62 = -25.132741632083
x63 = 25.1327410188866
x64 = 3.14159244884412
x65 = -3.14159311568248
x66 = 59.6902605976901
x67 = -40.8407046898283
x68 = -50.2654822953391
x69 = -12.5663700417108
x70 = -31.4159267051849
x71 = 15.7079634406648
x72 = -69.1150386737158
x73 = 47.123890018392
x74 = 21.9911485851964
x75 = 53.4070753627408
x76 = 9.42477859080277
x77 = 78.5398161878405
x78 = 28.2743338652012
x79 = 81.6814091761104
x80 = -21.9911485864515
x81 = 62.8318524523063
x82 = -59.6902604576401
x83 = 65.9734457528975
x84 = -81.6814090380061
x85 = 100.530964766599
x86 = -40.8407042660168
x87 = 87.9645943357576
x88 = 84.8230014093114
x89 = -91.106187201329
x90 = 18.8495556796107
x91 = 12.5663704518704
x92 = -34.5575189701076
x93 = 43.982297169427
x93 = 43.982297169427
Gráfico
sin(x)^2=0 la ecuación