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- La ecuación:
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Ecuación (x-3)*(x+2)=0
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Ecuación (11x+14)-(5x-8)=25
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Ecuación z^2-6*z+10=0
-
Ecuación 4/(x-4)=-5
- Expresar {x} en función de y en la ecuación:
- -7*x-13*y=5
- 15*x+1*y=19
- 7*x-1*y=-7
- -11*x-14*y=-3
- Integral de d{x}:
- sin2(x)
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Expresiones idénticas
- sin2(x)
- seno de 2(x)
- sin2x
-
Expresiones semejantes
- sin(2*x)-sin(x)=0
- 3sin^2(x)+4sin(x)cos(x)+cos^2(x)=0
- sin(2*x+pi/2)=0
- sin2x=-1/2
- sin(2*x)+cos(x)=0
sin2(x) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
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
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
Como D = 0 hay sólo una raíz.
$$w_{1} = 0$$
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:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$x_{1} = 2 \pi n$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
$$x_{2} = 2 \pi n + \pi$$
$$\sin^{2}{\left(x \right)} = 0$$
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:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$x_{1} = 2 \pi n$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
$$x_{2} = 2 \pi n + \pi$$
Respuesta numérica
[src]
x1 = -40.8407046898283
x2 = -47.123890151099
x3 = 72.256631027719
x4 = -78.5398160958028
x5 = 91.1061871583643
x6 = -1734.15914475848
x7 = -18.8495561207399
x8 = -12.5663703661411
x9 = -59.6902604576401
x10 = 100.530964766599
x11 = 9.42477859080277
x12 = -34.5575189426108
x13 = -47.1238900492539
x14 = 12.5663704518704
x15 = -106.814150357553
x16 = -12.5663700417108
x17 = -97.3893724403711
x18 = 43.982297169427
x19 = -43.9822971745789
x20 = 18.8495554002244
x21 = -69.1150386737158
x22 = -84.82300141007
x23 = 25.1327410188866
x24 = -65.9734457650176
x25 = 15.7079634406648
x26 = -53.4070752836338
x27 = 81.6814091761104
x28 = 84.8230014093114
x29 = 62.8318528326557
x30 = 56.5486676091327
x31 = -34.5575189701076
x32 = 75.3982239388525
x33 = 9.42477821024198
x34 = 50.2654824463473
x35 = -87.9645943587732
x36 = -6.28318513794069
x37 = 53.4070756765307
x38 = -21.9911485864515
x39 = 37.6991120192083
x40 = 62.8318524523063
x41 = 40.840703919946
x42 = 3.14159287686128
x43 = 18.8495556796107
x44 = 78.5398161878405
x45 = -94.2477794529919
x46 = -81.6814090380061
x47 = -62.8318528379059
x48 = -69.1150386253436
x49 = -37.6991118771514
x50 = 25.1327414478072
x51 = -25.132741632083
x52 = 6.28318528425126
x53 = -100.530964672522
x54 = 87.9645943357576
x55 = 97.3893725148693
x56 = -40.8407042660168
x57 = -31.4159267051849
x58 = -31.4159267959754
x59 = 47.123889589354
x60 = 0.0
x61 = -84.8230018263493
x62 = -15.7079632965264
x63 = -62.8318532583801
x64 = -3.14159289677385
x65 = -72.2566308741333
x66 = 91.1061867314459
x67 = 69.1150385885879
x68 = -9.42477812668337
x69 = 47.123890018392
x70 = 75.3982241944528
x71 = 3.14159244884412
x72 = 40.8407042560881
x73 = -25.132741473063
x74 = -91.106187201329
x75 = -50.2654822953391
x76 = 94.2477796093525
x77 = 34.5575190304759
x78 = 21.9911485851964
x79 = 65.9734457528975
x80 = -91.1061872003049
x81 = 69.1150381602162
x82 = -56.5486675191652
x83 = 84.8230010166547
x84 = -18.8495556944209
x85 = -3.14159311568248
x86 = 31.4159267865366
x87 = 59.6902605976901
x88 = 97.3893727097471
x89 = 53.4070753627408
x90 = 28.2743338652012
x91 = -28.2743337166085
x92 = 31.4159271479423
x93 = -75.3982238620294
x93 = -75.3982238620294