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sin(x)+sqrt((2-sqrt3)/2*(cos(x)+1))=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
              ________________________    
             /       ___                  
            /  2 - \/ 3                   
sin(x) +   /   ---------*(cos(x) + 1)  = 0
         \/        2                      
$$\sqrt{\frac{2 - \sqrt{3}}{2} \left(\cos{\left(x \right)} + 1\right)} + \sin{\left(x \right)} = 0$$
Gráfica
Suma y producto de raíces [src]
suma
       /   ___________\
       |  /       ___ |
       |\/  2 - \/ 3  |
-2*atan|--------------|
       |   ___________|
       |  /       ___ |
       \\/  2 + \/ 3  /
$$- 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{3}}}{\sqrt{\sqrt{3} + 2}} \right)}$$
=
       /   ___________\
       |  /       ___ |
       |\/  2 - \/ 3  |
-2*atan|--------------|
       |   ___________|
       |  /       ___ |
       \\/  2 + \/ 3  /
$$- 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{3}}}{\sqrt{\sqrt{3} + 2}} \right)}$$
producto
       /   ___________\
       |  /       ___ |
       |\/  2 - \/ 3  |
-2*atan|--------------|
       |   ___________|
       |  /       ___ |
       \\/  2 + \/ 3  /
$$- 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{3}}}{\sqrt{\sqrt{3} + 2}} \right)}$$
=
       /   ___________\
       |  /       ___ |
       |\/  2 - \/ 3  |
-2*atan|--------------|
       |   ___________|
       |  /       ___ |
       \\/  2 + \/ 3  /
$$- 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{3}}}{\sqrt{\sqrt{3} + 2}} \right)}$$
-2*atan(sqrt(2 - sqrt(3))/sqrt(2 + sqrt(3)))
Respuesta rápida [src]
            /   ___________\
            |  /       ___ |
            |\/  2 - \/ 3  |
x1 = -2*atan|--------------|
            |   ___________|
            |  /       ___ |
            \\/  2 + \/ 3  /
$$x_{1} = - 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{3}}}{\sqrt{\sqrt{3} + 2}} \right)}$$
x1 = -2*atan(sqrt(2 - sqrt(3))/sqrt(sqrt(3) + 2))
Respuesta numérica [src]
x1 = 162.839219211071
x2 = 59.6902604182061
x3 = 62.3082542961976
x4 = -25.6563400043166
x5 = -94.7713783832921
x6 = -15.707963267949
x7 = 84.8230016469244
x8 = 97.3893722612836
x9 = 5.75958653158129
x10 = 100.007366139275
x11 = -72.2566310325652
x12 = 91.106186954104
x13 = 87.4409955249159
x14 = -65.9734457253857
x15 = -69.6386371545737
x16 = 24.60914245312
x17 = -53.4070751110265
x18 = -31.9395253114962
x19 = -59.6902604182061
x20 = 30.8923277602996
x21 = 15.707963267949
x22 = -75.9218224617533
x23 = 9.42477796076938
x24 = -82.2050077689329
x25 = 43.4586983746588
x26 = 93.7241808320955
x27 = 37.1755130674792
x28 = 40.8407044966673
x29 = 68.5914396033772
x30 = -21.9911485751286
x31 = -84.8230016469244
x32 = 3.14159265358979
x33 = 18.3259571459405
x34 = -0.523598775598299
x35 = 74.8746249105567
x36 = 219.387886975687
x37 = -50.789081233035
x38 = 72.2566310325652
x39 = 21.9911485751286
x40 = 47.1238898038469
x41 = 34.5575191894877
x42 = -97.3893722612836
x43 = -78.5398163397448
x44 = -47.1238898038469
x45 = -57.0722665402146
x46 = 28.2743338823081
x47 = -40.8407044966673
x48 = -44.5058959258554
x49 = -34.5575191894877
x50 = -28.2743338823081
x51 = -88.4881930761125
x52 = 78.5398163397448
x53 = -13.0899693899575
x54 = -101.054563690472
x55 = -14948.2214445558
x56 = -91.106186954104
x57 = 56.025068989018
x58 = -38.2227106186758
x59 = 49.7418836818384
x60 = -6.80678408277789
x61 = 81.1578102177363
x62 = -19.3731546971371
x63 = -3.14159265358979
x64 = -258.134196369961
x65 = 53.4070751110265
x66 = 12.0427718387609
x67 = 65.9734457253857
x68 = -9.42477796076938
x69 = -63.3554518473942
x69 = -63.3554518473942