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sin(pi*x/2)=-1 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   /pi*x\     
sin|----| = -1
   \ 2  /
sin⁡(πx2)=−1\sin{\left(\frac{\pi x}{2} \right)} = -1
Simplificar
Solución detallada
Tenemos la ecuación
sin⁡(πx2)=−1\sin{\left(\frac{\pi x}{2} \right)} = -1
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
πx2=2πn+asin⁡(−1)\frac{\pi x}{2} = 2 \pi n + \operatorname{asin}{\left(-1 \right)}
πx2=2πn−asin⁡(−1)+π\frac{\pi x}{2} = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi
O
πx2=2πn−π2\frac{\pi x}{2} = 2 \pi n - \frac{\pi}{2}
πx2=2πn+3π2\frac{\pi x}{2} = 2 \pi n + \frac{3 \pi}{2}
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
π2\frac{\pi}{2}
obtenemos la respuesta:
x1=2(2πn−π2)πx_{1} = \frac{2 \left(2 \pi n - \frac{\pi}{2}\right)}{\pi}
x2=2(2πn+3π2)πx_{2} = \frac{2 \left(2 \pi n + \frac{3 \pi}{2}\right)}{\pi}
Gráfica
0-80-60-40-2020406080-1001002-2
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
-1 + 3
−1+3-1 + 3 
=
2
22 
producto
-3
−3- 3 
=
-3
−3-3 
-3
Respuesta rápida [src] 
x1 = -1
x1=−1x_{1} = -1 
x2 = 3
x2=3x_{2} = 3 
x2 = 3
Respuesta numérica [src] 
x1 = 6.99999969529569
x2 = -29.0000003047043
x3 = -77.0000003047043
x4 = 58.9999996952957
x5 = 27.0000003211474
x6 = -25.0000003047043
x7 = -60.9999996788526
x8 = 98.9999996952957
x9 = -52.9999996788526
x10 = -53.0000003047043
x11 = 23.0000003211474
x12 = -97.0000003047043
x13 = 39.0000003211474
x14 = 10.9999996952957
x15 = -56.9999996788526
x16 = -33.0000003047043
x17 = -41.0000003047043
x18 = 74.9999996952957
x19 = 50.9999996952957
x20 = 82.9999996952957
x21 = -88.9999996788525
x22 = 14.9999996952957
x23 = 26.9999996952957
x24 = 59.0000003211474
x25 = -84.9999996788525
x26 = -16.9999996788526
x27 = 47.0000003211474
x28 = 55.0000003211474
x29 = -17.0000003047043
x30 = -0.999999678852552
x31 = -57.0000003047043
x32 = -20.9999996788526
x33 = 95.0000003211475
x34 = -40.9999996788526
x35 = -21.0000003047043
x36 = 42.9999996952957
x37 = 62.9999996952957
x38 = 66.9999996952957
x39 = -65.0000003047043
x40 = -13.0000003047043
x41 = 3.00000032114745
x42 = 99.0000003211475
x43 = -92.9999996788525
x44 = 54.9999996952957
x45 = -49.0000003047043
x46 = -76.9999996788525
x47 = 31.0000003211474
x48 = -81.0000003047043
x49 = -80.9999996788525
x50 = 15.0000003211474
x51 = -4.99999967885255
x52 = 7.00000032114745
x53 = 90.9999996952957
x54 = 46.9999996952957
x55 = 94.9999996952957
x56 = 63.0000003211474
x57 = 2.99999969529569
x58 = 51.0000003211474
x59 = 83.0000003211475
x60 = 30.9999996952957
x61 = -85.0000003047043
x62 = 43.0000003211474
x63 = -45.0000003047043
x64 = -89.0000003047043
x65 = 34.9999996952957
x66 = -36.9999996788526
x67 = 11.0000003211474
x68 = -8.99999967885255
x69 = -61.0000003047043
x70 = -32.9999996788526
x71 = 86.9999996952957
x72 = 22.9999996952957
x73 = -73.0000003047043
x74 = 67.0000003211475
x75 = 35.0000003211474
x76 = 87.0000003211475
x77 = 91.0000003211475
x78 = 79.0000003211475
x79 = -12.9999996788526
x80 = -24.9999996788526
x81 = -100.999999678853
x82 = -72.9999996788525
x83 = 71.0000003211475
x84 = 78.9999996952957
x85 = 75.0000003211475
x86 = -5.00000030470431
x87 = -44.9999996788526
x88 = 70.9999996952957
x89 = -9.00000030470431
x90 = -69.0000003047043
x91 = -96.9999996788525
x92 = -48.9999996788526
x93 = -28.9999996788526
x94 = 19.0000003211474
x95 = 18.9999996952957
x96 = -37.0000003047043
x97 = -68.9999996788525
x98 = -64.9999996788525
x99 = -93.0000003047043
x100 = 38.9999996952957
x101 = -1.00000030470431
x101 = -1.00000030470431
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