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cos(x)=-(sqrt(3)/3) la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
            ___ 
         -\/ 3  
cos(x) = -------
            3   
$$\cos{\left(x \right)} = - \frac{\sqrt{3}}{3}$$
Solución detallada
Tenemos la ecuación
$$\cos{\left(x \right)} = - \frac{\sqrt{3}}{3}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)}$$
O
$$x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)}$$
, donde n es cualquier número entero
Gráfica
Respuesta rápida [src]
           /   ___ \       
           |-\/ 3  |       
x1 = - acos|-------| + 2*pi
           \   3   /       
$$x_{1} = - \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)} + 2 \pi$$
         /   ___ \
         |-\/ 3  |
x2 = acos|-------|
         \   3   /
$$x_{2} = \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)}$$
x2 = acos(-sqrt(3)/3)
Suma y producto de raíces [src]
suma
      /   ___ \              /   ___ \
      |-\/ 3  |              |-\/ 3  |
- acos|-------| + 2*pi + acos|-------|
      \   3   /              \   3   /
$$\operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)} + \left(- \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)} + 2 \pi\right)$$
=
2*pi
$$2 \pi$$
producto
/      /   ___ \       \     /   ___ \
|      |-\/ 3  |       |     |-\/ 3  |
|- acos|-------| + 2*pi|*acos|-------|
\      \   3   /       /     \   3   /
$$\left(- \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)}$$
=
/      /   ___ \       \     /   ___ \
|      |-\/ 3  |       |     |-\/ 3  |
|- acos|-------| + 2*pi|*acos|-------|
\      \   3   /       /     \   3   /
$$\left(- \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{\sqrt{3}}{3} \right)}$$
(-acos(-sqrt(3)/3) + 2*pi)*acos(-sqrt(3)/3)
Respuesta numérica [src]
x1 = 2.18627603546528
x2 = -98.3446888794081
x3 = -14.7526466498245
x4 = -60.6455770363306
x5 = -92.0615035722285
x6 = -41.7960211147918
x7 = -52.451758492902
x8 = 79.4951329578693
x9 = 22.9464651932531
x10 = 16.6632798860735
x11 = 4.0969092717143
x12 = -73.2119476506898
x13 = 21.035831957004
x14 = 33.6022025713632
x15 = -79.4951329578693
x16 = -46.1685731857224
x17 = -2.18627603546528
x18 = -21.035831957004
x19 = 35.5128358076122
x20 = 77.5844997216203
x21 = 39.8853878785428
x22 = 65.0181291072611
x23 = -71.3013144144407
x24 = 83.8676850287999
x25 = 27.3190172641836
x26 = -35.5128358076122
x27 = 96.4340556431591
x28 = 46.1685731857224
x29 = 73.2119476506898
x30 = 41.7960211147918
x31 = -39.8853878785428
x32 = -29.2296505004326
x33 = -48.0792064219714
x34 = 52.451758492902
x35 = 8.46946134264487
x36 = 60.6455770363306
x37 = -66.9287623435102
x38 = 92.0615035722285
x39 = -58.7349438000816
x40 = -77.5844997216203
x41 = 66.9287623435102
x42 = -54.362391729151
x43 = -96.4340556431591
x44 = -8.46946134264487
x45 = -65.0181291072611
x46 = 58.7349438000816
x47 = -83.8676850287999
x48 = -85.7783182650489
x49 = -16.6632798860735
x50 = 14.7526466498245
x51 = 98.3446888794081
x52 = 54.362391729151
x53 = -27.3190172641836
x54 = 90.1508703359795
x55 = 85.7783182650489
x56 = -10.3800945788939
x57 = 48.0792064219714
x58 = 29.2296505004326
x59 = 10.3800945788939
x60 = -33.6022025713632
x61 = -4.0969092717143
x62 = 71.3013144144407
x63 = -22.9464651932531
x64 = -90.1508703359795
x64 = -90.1508703359795