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Solución de sistemas de ecuaciones/ sinx+cosy=1; sin^2(x)+2*sinx*cosy=3/4

sinx+cosy=1; sin^2(x)+2*sinx*cosy=3/4

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Gráfico:

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Solución

Ha introducido [src] 
sin(x) + cos(y) = 1
sin⁡(x)+cos⁡(y)=1\sin{\left(x \right)} + \cos{\left(y \right)} = 1 
   2                           
sin (x) + 2*sin(x)*cos(y) = 3/4
sin⁡2(x)+2sin⁡(x)cos⁡(y)=34\sin^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(y \right)} = \frac{3}{4} 
sin(x)^2 + (2*sin(x))*cos(y) = 3/4
Respuesta rápida
x1=π6x_{1} = \frac{\pi}{6}
=
π6\frac{\pi}{6}
=
0.523598775598299

y1=π3y_{1} = \frac{\pi}{3}
=
π3\frac{\pi}{3}
=
1.04719755119660
x2=π6x_{2} = \frac{\pi}{6}
=
π6\frac{\pi}{6}
=
0.523598775598299

y2=5π3y_{2} = \frac{5 \pi}{3}
=
5π3\frac{5 \pi}{3}
=
5.23598775598299
x3=5π6x_{3} = \frac{5 \pi}{6}
=
5π6\frac{5 \pi}{6}
=
2.61799387799149

y3=π3y_{3} = \frac{\pi}{3}
=
π3\frac{\pi}{3}
=
1.04719755119660
x4=5π6x_{4} = \frac{5 \pi}{6}
=
5π6\frac{5 \pi}{6}
=
2.61799387799149

y4=5π3y_{4} = \frac{5 \pi}{3}
=
5π3\frac{5 \pi}{3}
=
5.23598775598299
x5=π−asin⁡(32)x_{5} = \pi - \operatorname{asin}{\left(\frac{3}{2} \right)}
=
π−asin⁡(32)\pi - \operatorname{asin}{\left(\frac{3}{2} \right)}
=
1.5707963267949 + 0.962423650119207*i

y5=2π3y_{5} = \frac{2 \pi}{3}
=
2π3\frac{2 \pi}{3}
=
2.09439510239320
x6=π−asin⁡(32)x_{6} = \pi - \operatorname{asin}{\left(\frac{3}{2} \right)}
=
π−asin⁡(32)\pi - \operatorname{asin}{\left(\frac{3}{2} \right)}
=
1.5707963267949 + 0.962423650119207*i

y6=4π3y_{6} = \frac{4 \pi}{3}
=
4π3\frac{4 \pi}{3}
=
4.18879020478639
x7=asin⁡(32)x_{7} = \operatorname{asin}{\left(\frac{3}{2} \right)}
=
asin⁡(32)\operatorname{asin}{\left(\frac{3}{2} \right)}
=
1.5707963267949 - 0.962423650119207*i

y7=2π3y_{7} = \frac{2 \pi}{3}
=
2π3\frac{2 \pi}{3}
=
2.09439510239320
x8=asin⁡(32)x_{8} = \operatorname{asin}{\left(\frac{3}{2} \right)}
=
asin⁡(32)\operatorname{asin}{\left(\frac{3}{2} \right)}
=
1.5707963267949 - 0.962423650119207*i

y8=4π3y_{8} = \frac{4 \pi}{3}
=
4π3\frac{4 \pi}{3}
=
4.18879020478639
Respuesta numérica [src] 
x1 = -5.759586531581288
y1 = -5.235987755982989
x2 = 0.5235987755982989
y2 = -5.235987755982989
x3 = 0.5235987755982989
y3 = 5.235987755982989
x4 = -9.948376736367678
y4 = 11.51917306316258
x5 = -5.759586531581288
y5 = 1.047197551196598
x6 = 2.617993877991494
y6 = 13.61356816555577
x7 = -9.948376736367678
y7 = -1.047197551196598
x8 = -9.948376736367678
y8 = -11.51917306316258
x9 = -5.759586531581288
y9 = 5.235987755982989
x10 = 6.806784082777885
y10 = 5.235987755982989
x11 = -9.948376736367678
y11 = 5.235987755982989
x12 = -9.948376736367678
y12 = 1.047197551196598
x13 = -5.759586531581288
y13 = 13.61356816555577
x14 = 8.901179185171081
y14 = 13.61356816555577
x15 = -9.948376736367678
y15 = -5.235987755982989
x16 = -5.759586531581288
y16 = -1.047197551196598
x16 = -5.759586531581288
y16 = -1.047197551196598
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