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sin(2*x/3)=-sqrt(2)/2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
              ___ 
   /2*x\   -\/ 2  
sin|---| = -------
   \ 3 /      2   
$$\sin{\left(\frac{2 x}{3} \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
Solución detallada
Tenemos la ecuación
$$\sin{\left(\frac{2 x}{3} \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$\frac{2 x}{3} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$\frac{2 x}{3} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)} + \pi$$
O
$$\frac{2 x}{3} = 2 \pi n - \frac{\pi}{4}$$
$$\frac{2 x}{3} = 2 \pi n + \frac{5 \pi}{4}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$\frac{2}{3}$$
obtenemos la respuesta:
$$x_{1} = 3 \pi n - \frac{3 \pi}{8}$$
$$x_{2} = 3 \pi n + \frac{15 \pi}{8}$$
Gráfica
Suma y producto de raíces [src]
suma
  3*pi   15*pi
- ---- + -----
   8       8  
$$- \frac{3 \pi}{8} + \frac{15 \pi}{8}$$
=
3*pi
----
 2  
$$\frac{3 \pi}{2}$$
producto
-3*pi 15*pi
-----*-----
  8     8  
$$- \frac{3 \pi}{8} \frac{15 \pi}{8}$$
=
      2
-45*pi 
-------
   64  
$$- \frac{45 \pi^{2}}{64}$$
-45*pi^2/64
Respuesta rápida [src]
     -3*pi
x1 = -----
       8  
$$x_{1} = - \frac{3 \pi}{8}$$
     15*pi
x2 = -----
       8  
$$x_{2} = \frac{15 \pi}{8}$$
x2 = 15*pi/8
Respuesta numérica [src]
x1 = 5.89048622548086
x2 = 100.138265833175
x3 = 36.5210145979813
x4 = -3.53429173528852
x5 = -50.6581815391354
x6 = 8.24668071567321
x7 = -1.17809724509617
x8 = -97.7820713429823
x9 = -69.5077374606742
x10 = -76.5763209312512
x11 = 15.3152641862502
x12 = 34.164820107789
x13 = -88.3572933822129
x14 = 45.9457925587507
x15 = -60.0829594999048
x16 = 81.2887099116359
x17 = 64.7953484802895
x18 = 17.6714586764426
x19 = 74.2201264410589
x20 = 43.5895980685584
x21 = 102.494460323367
x22 = -12.9590696960579
x23 = -41.233403578366
x24 = -22.3838476568273
x25 = -67.1515429704818
x26 = 63757.4448073598
x27 = -29.4524311274043
x28 = -48.3019870489431
x29 = -86.0010988920206
x30 = 83.6449044018282
x31 = -20.0276531666349
x32 = 71.8639319508665
x33 = 24.7400421470196
x34 = -31.8086256175967
x35 = -57.7267650097125
x36 = -465.348411812988
x37 = 93.0696823625976
x38 = 27.096236637212
x39 = 53.0143760293278
x40 = 90.7134878724053
x41 = 55.3705705195201
x42 = -78.9325154214436
x43 = -38.8772090881737
x44 = 62.4391539900971
x45 = 583.158136322605
x46 = -95.42587685279
x47 = -434.717883440488
x48 = -10.6028752058656
x48 = -10.6028752058656