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cos(x)=-(sqrt(2))/2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
            ___ 
         -\/ 2  
cos(x) = -------
            2   
$$\cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
Solución detallada
Tenemos la ecuación
$$\cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
O
$$x = \pi n + \frac{3 \pi}{4}$$
$$x = \pi n - \frac{\pi}{4}$$
, donde n es cualquier número entero
Gráfica
Suma y producto de raíces [src]
suma
3*pi   5*pi
---- + ----
 4      4  
$$\frac{3 \pi}{4} + \frac{5 \pi}{4}$$
=
2*pi
$$2 \pi$$
producto
3*pi 5*pi
----*----
 4    4  
$$\frac{3 \pi}{4} \frac{5 \pi}{4}$$
=
     2
15*pi 
------
  16  
$$\frac{15 \pi^{2}}{16}$$
15*pi^2/16
Respuesta rápida [src]
     3*pi
x1 = ----
      4  
$$x_{1} = \frac{3 \pi}{4}$$
     5*pi
x2 = ----
      4  
$$x_{2} = \frac{5 \pi}{4}$$
x2 = 5*pi/4
Respuesta numérica [src]
x1 = -79.3252145031423
x2 = -66.7588438887831
x3 = -73.0420291959627
x4 = -85.6083998103219
x5 = -21.2057504117311
x6 = -10.2101761241668
x7 = -335.36501577071
x8 = 41.6261026600648
x9 = -29.0597320457056
x10 = 90.3207887907066
x11 = -35.3429173528852
x12 = 21.2057504117311
x13 = 2.35619449019234
x14 = 8.63937979737193
x15 = -60.4756585816035
x16 = -52.621676947629
x17 = 255.254403104171
x18 = 79.3252145031423
x19 = 3.92699081698724
x20 = 35.3429173528852
x21 = -46.3384916404494
x22 = 60.4756585816035
x23 = -27.4889357189107
x24 = -2.35619449019234
x25 = 29.0597320457056
x26 = 71.4712328691678
x27 = -90.3207887907066
x28 = 39349.2333843756
x29 = 14.9225651045515
x30 = 47.9092879672443
x31 = -77.7544181763474
x32 = 33.7721210260903
x33 = 73.0420291959627
x34 = 77.7544181763474
x35 = -54.1924732744239
x36 = 54.1924732744239
x37 = 46.3384916404494
x38 = -47.9092879672443
x39 = -65.1880475619882
x40 = 2584.745355741
x41 = 96.6039740978861
x42 = 66.7588438887831
x43 = -96.6039740978861
x44 = 65.1880475619882
x45 = 104.457955731861
x46 = 85.6083998103219
x47 = 16.4933614313464
x48 = -71.4712328691678
x49 = -8.63937979737193
x50 = -3.92699081698724
x51 = 27.4889357189107
x52 = 98.174770424681
x53 = 52.621676947629
x54 = -14.9225651045515
x55 = -40.0553063332699
x56 = 22.776546738526
x57 = -41.6261026600648
x58 = -16.4933614313464
x59 = 40.0553063332699
x60 = 58.9048622548086
x61 = -58.9048622548086
x62 = -84.037603483527
x63 = 91.8915851175014
x64 = -33.7721210260903
x65 = 10.2101761241668
x66 = -22.776546738526
x67 = -98.174770424681
x68 = 84.037603483527
x69 = -91.8915851175014
x69 = -91.8915851175014