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cos(x)=-√2/2

cos(x)=-√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
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
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 numérica [src]
x1 = 21.2057504117311
x2 = 35.3429173528852
x3 = -14.9225651045515
x4 = 40.0553063332699
x5 = 29.0597320457056
x6 = 2.35619449019234
x7 = 85.6083998103219
x8 = 39349.2333843756
x9 = -3.92699081698724
x10 = 65.1880475619882
x11 = -16.4933614313464
x12 = 104.457955731861
x13 = 66.7588438887831
x14 = -8.63937979737193
x15 = -335.36501577071
x16 = 71.4712328691678
x17 = -71.4712328691678
x18 = -73.0420291959627
x19 = 8.63937979737193
x20 = 22.776546738526
x21 = -85.6083998103219
x22 = -46.3384916404494
x23 = -98.174770424681
x24 = 33.7721210260903
x25 = -54.1924732744239
x26 = 79.3252145031423
x27 = 255.254403104171
x28 = 77.7544181763474
x29 = 73.0420291959627
x30 = -79.3252145031423
x31 = -27.4889357189107
x32 = -22.776546738526
x33 = -96.6039740978861
x34 = 84.037603483527
x35 = -47.9092879672443
x36 = -52.621676947629
x37 = -29.0597320457056
x38 = -21.2057504117311
x39 = -41.6261026600648
x40 = 14.9225651045515
x41 = -84.037603483527
x42 = -60.4756585816035
x43 = 98.174770424681
x44 = 96.6039740978861
x45 = -91.8915851175014
x46 = 91.8915851175014
x47 = -65.1880475619882
x48 = -66.7588438887831
x49 = 10.2101761241668
x50 = 52.621676947629
x51 = -77.7544181763474
x52 = 41.6261026600648
x53 = -35.3429173528852
x54 = 46.3384916404494
x55 = 60.4756585816035
x56 = -40.0553063332699
x57 = 2584.745355741
x58 = 90.3207887907066
x59 = -58.9048622548086
x60 = -2.35619449019234
x61 = 54.1924732744239
x62 = 3.92699081698724
x63 = -10.2101761241668
x64 = -90.3207887907066
x65 = -33.7721210260903
x66 = 16.4933614313464
x67 = 27.4889357189107
x68 = 58.9048622548086
x69 = 47.9092879672443
x69 = 47.9092879672443
Gráfico
cos(x)=-√2/2 la ecuación