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sqrt(sin(x)-1)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
  ____________    
\/ sin(x) - 1  = 0
sin⁡(x)−1=0\sqrt{\sin{\left(x \right)} - 1} = 0
Simplificar
Solución detallada
Tenemos la ecuación
sin⁡(x)−1=0\sqrt{\sin{\left(x \right)} - 1} = 0
cambiamos
sin⁡(x)−1=0\sqrt{\sin{\left(x \right)} - 1} = 0
sin⁡(x)−1=0\sqrt{\sin{\left(x \right)} - 1} = 0
Sustituimos
w=sin⁡(x)w = \sin{\left(x \right)}
Tenemos la ecuación
w−1=0\sqrt{w - 1} = 0
es decir
w−1=0w - 1 = 0
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
w=1w = 1
Obtenemos la respuesta: w = 1
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=2πn−asin⁡(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=2πn−asin⁡(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⁡(1)x_{1} = 2 \pi n + \operatorname{asin}{\left(1 \right)}
x1=2πn+π2x_{1} = 2 \pi n + \frac{\pi}{2}
x2=2πn−asin⁡(w1)+πx_{2} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi
x2=2πn−asin⁡(1)+πx_{2} = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi
x2=2πn+π2x_{2} = 2 \pi n + \frac{\pi}{2}
Gráfica
0-80-60-40-2020406080-10010001
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
pi
--
2
π2\frac{\pi}{2} 
=
pi
--
2
π2\frac{\pi}{2} 
producto
pi
--
2
π2\frac{\pi}{2} 
=
pi
--
2
π2\frac{\pi}{2} 
pi/2
Respuesta rápida [src] 
     pi
x1 = --
     2
x1=π2x_{1} = \frac{\pi}{2} 
x1 = pi/2
Respuesta numérica [src] 
x1 = -180.641577581413
x2 = 7.85398163397448
x3 = -54.9778714378214
x4 = -73.8274273593601
x5 = 76.96902001295
x6 = -4.71238898038469
x7 = 14.1371669411541
x8 = 58.1194640914112
x9 = 70.6858347057703
x10 = -36.1283155162826
x11 = 39.2699081698724
x12 = -92.6769832808989
x13 = -4.7123889803847
x14 = -86.3937979737193
x15 = -54.9778714378214
x16 = 39.2699081698724
x17 = -10.9955742875643
x18 = -10.9955742875643
x19 = 108.384946548848
x20 = 83.2522053201295
x21 = -61.261056745001
x22 = -67.5442420521806
x23 = 26.7035375555132
x24 = -48.6946861306418
x25 = 51.8362787842316
x26 = -42.4115008234622
x27 = -98.9601685880785
x28 = 95.8185759344887
x29 = 1.5707963267949
x30 = 45.553093477052
x31 = -17.2787595947439
x32 = 76.9690200129499
x33 = 215.199096770901
x34 = 20.4203522483337
x35 = -80.1106126665397
x36 = 32.9867228626928
x37 = -48.6946861306418
x38 = -23.5619449019235
x39 = 32.9867228626928
x40 = 64.4026493985908
x41 = 89.5353906273091
x42 = -92.6769832808989
x43 = -29.845130209103
x44 = 83.2522053201295
x44 = 83.2522053201295
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