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sinx⋅cosx=(√2/2)sinx la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                  ___       
                \/ 2        
sin(x)*cos(x) = -----*sin(x)
                  2
$$\sin{\left(x \right)} \cos{\left(x \right)} = \frac{\sqrt{2}}{2} \sin{\left(x \right)}$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
x1 = 0
$$x_{1} = 0$$ 
            /   ___________\
            |  /       ___ |
            |\/  2 - \/ 2  |
x2 = -2*atan|--------------|
            |   ___________|
            |  /       ___ |
            \\/  2 + \/ 2  /
$$x_{2} = - 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)}$$ 
           /   ___________\
           |  /       ___ |
           |\/  2 - \/ 2  |
x3 = 2*atan|--------------|
           |   ___________|
           |  /       ___ |
           \\/  2 + \/ 2  /
$$x_{3} = 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)}$$ 
x3 = 2*atan(sqrt(2 - sqrt(2))/sqrt(sqrt(2) + 2))
Suma y producto de raíces [src] 
suma
        /   ___________\         /   ___________\
        |  /       ___ |         |  /       ___ |
        |\/  2 - \/ 2  |         |\/  2 - \/ 2  |
- 2*atan|--------------| + 2*atan|--------------|
        |   ___________|         |   ___________|
        |  /       ___ |         |  /       ___ |
        \\/  2 + \/ 2  /         \\/  2 + \/ 2  /
$$- 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)} + 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)}$$ 
=
0
$$0$$ 
producto
         /   ___________\       /   ___________\
         |  /       ___ |       |  /       ___ |
         |\/  2 - \/ 2  |       |\/  2 - \/ 2  |
0*-2*atan|--------------|*2*atan|--------------|
         |   ___________|       |   ___________|
         |  /       ___ |       |  /       ___ |
         \\/  2 + \/ 2  /       \\/  2 + \/ 2  /
$$0 \left(- 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)}\right) 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)}$$ 
=
0
$$0$$ 
0
Respuesta numérica [src] 
x1 = 18.0641577581413
x2 = 25.9181393921158
x3 = 63.6172512351933
x4 = -106.814150222053
x5 = 59.6902604182061
x6 = -13.3517687777566
x7 = -62.0464549083984
x8 = 44.7676953136546
x9 = -51.0508806208341
x10 = 57.3340659280137
x11 = -24.3473430653209
x12 = 34.5575191894877
x13 = -21.9911485751286
x14 = 15.707963267949
x15 = 19.6349540849362
x16 = -91.106186954104
x17 = -30.6305283725005
x18 = -81.6814089933346
x19 = -63.6172512351933
x20 = 126.449104306989
x21 = -12.5663706143592
x22 = -94.2477796076938
x23 = -59.6902604182061
x24 = -43.9822971502571
x25 = 13.3517687777566
x26 = 32.2013246992954
x27 = 43.9822971502571
x28 = -57.3340659280137
x29 = -32.2013246992954
x30 = 30.6305283725005
x31 = -3.14159265358979
x32 = -15.707963267949
x33 = 9.42477796076938
x34 = 76.1836218495525
x35 = 80.8960108299372
x36 = 7.06858347057703
x37 = 0.0
x38 = -65.9734457253857
x39 = -74.6128255227576
x40 = 690.364985626357
x41 = -28.2743338823081
x42 = -7.06858347057703
x43 = 99.7455667514759
x44 = -80.8960108299372
x45 = -19.6349540849362
x46 = 28.2743338823081
x47 = 65.9734457253857
x48 = 40.8407044966673
x49 = -76.1836218495525
x50 = -36.9137136796801
x51 = 68.329640215578
x52 = -47.1238898038469
x53 = -87.9645943005142
x54 = -11.7809724509617
x55 = 36.9137136796801
x56 = 426.471202724814
x57 = 62.0464549083984
x58 = -25.9181393921158
x59 = -5.49778714378214
x60 = -97.3893722612836
x61 = 94.2477796076938
x62 = 84.8230016469244
x63 = 72.2566310325652
x64 = -55.7632696012188
x65 = -106.028752058656
x66 = 11.7809724509617
x67 = -9.42477796076938
x68 = 74.6128255227576
x69 = -99.7455667514759
x70 = -18.0641577581413
x71 = 6.28318530717959
x72 = -53.4070751110265
x73 = 21.9911485751286
x74 = 87.9645943005142
x75 = -72.2566310325652
x76 = -68.329640215578
x77 = 50.2654824574367
x78 = -69.9004365423729
x79 = 53.4070751110265
x80 = 69.9004365423729
x81 = 97.3893722612836
x82 = 24.3473430653209
x83 = -37.6991118430775
x84 = 78.5398163397448
x85 = -78.5398163397448
x86 = 106.028752058656
x87 = 14551.8571714279
x88 = -95.0331777710912
x89 = -34.5575191894877
x90 = 87.1791961371168
x90 = 87.1791961371168
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