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sin^2(x)=0

sin^2(x)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
   2       
sin (x) = 0
$$\sin^{2}{\left(x \right)} = 0$$
Solución detallada
Tenemos la ecuación
$$\sin^{2}{\left(x \right)} = 0$$
cambiamos
$$\sin^{2}{\left(x \right)} = 0$$
$$\sin^{2}{\left(x \right)} = 0$$
Sustituimos
$$w = \sin{\left(x \right)}$$
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:
$$w_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$w_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 1$$
$$b = 0$$
$$c = 0$$
, 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)

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