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cosx-sin((pi/2)-x)+cos(pi+x)=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
            /pi    \                  
cos(x) - sin|-- - x| + cos(pi + x) = 0
            \2     /                  
$$\left(- \sin{\left(- x + \frac{\pi}{2} \right)} + \cos{\left(x \right)}\right) + \cos{\left(x + \pi \right)} = 0$$
Solución detallada
Tenemos la ecuación
$$\left(- \sin{\left(- x + \frac{\pi}{2} \right)} + \cos{\left(x \right)}\right) + \cos{\left(x + \pi \right)} = 0$$
es la ecuación trigonométrica más simple
cambiando el signo de 0

Obtenemos:
$$\left(- \sin{\left(- x + \frac{\pi}{2} \right)} + \cos{\left(x \right)}\right) + \cos{\left(x + \pi \right)} = 0$$
Dividamos ambos miembros de la ecuación en -1

La ecuación se convierte en
$$\cos{\left(x \right)} = 0$$
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
O
$$x = \pi n + \frac{\pi}{2}$$
$$x = \pi n - \frac{\pi}{2}$$
, donde n es cualquier número entero
Gráfica
Respuesta rápida [src]
     pi
x1 = --
     2 
$$x_{1} = \frac{\pi}{2}$$
     3*pi
x2 = ----
      2  
$$x_{2} = \frac{3 \pi}{2}$$
x2 = 3*pi/2
Suma y producto de raíces [src]
suma
pi   3*pi
-- + ----
2     2  
$$\frac{\pi}{2} + \frac{3 \pi}{2}$$
=
2*pi
$$2 \pi$$
producto
pi 3*pi
--*----
2   2  
$$\frac{\pi}{2} \frac{3 \pi}{2}$$
=
    2
3*pi 
-----
  4  
$$\frac{3 \pi^{2}}{4}$$
3*pi^2/4
Respuesta numérica [src]
x1 = 4.71238898038469
x2 = 17.2787595947439
x3 = -2266.65909956504
x4 = -89.5353906273091
x5 = 64.4026493985908
x6 = 70.6858347057703
x7 = 36.1283155162826
x8 = -98.9601685880785
x9 = 48.6946861306418
x10 = -58.1194640914112
x11 = 7.85398163397448
x12 = 39.2699081698724
x13 = -95.8185759344887
x14 = -1.5707963267949
x15 = -92.6769832808989
x16 = -23.5619449019235
x17 = 23.5619449019235
x18 = -387.986692718339
x19 = 61.261056745001
x20 = 29.845130209103
x21 = -32.9867228626928
x22 = -51.8362787842316
x23 = -80.1106126665397
x24 = -83.2522053201295
x25 = 67.5442420521806
x26 = 98.9601685880785
x27 = 92.6769832808989
x28 = -39.2699081698724
x29 = 86.3937979737193
x30 = 45.553093477052
x31 = -67.5442420521806
x32 = 51.8362787842316
x33 = 76.9690200129499
x34 = -26.7035375555132
x35 = -4.71238898038469
x36 = 95.8185759344887
x37 = -86.3937979737193
x38 = -10.9955742875643
x39 = 83.2522053201295
x40 = -7.85398163397448
x41 = -36.1283155162826
x42 = -17.2787595947439
x43 = -14.1371669411541
x44 = 20.4203522483337
x45 = 54.9778714378214
x46 = -168.075206967054
x47 = -70.6858347057703
x48 = -48.6946861306418
x49 = -54.9778714378214
x50 = -45.553093477052
x51 = 14.1371669411541
x52 = -73.8274273593601
x53 = 26.7035375555132
x54 = 89.5353906273091
x55 = 10.9955742875643
x56 = 80.1106126665397
x57 = 73.8274273593601
x58 = 58.1194640914112
x59 = -61.261056745001
x60 = 1.5707963267949
x61 = -20.4203522483337
x62 = -42.4115008234622
x63 = 32.9867228626928
x64 = 42.4115008234622
x65 = -76.9690200129499
x66 = -64.4026493985908
x67 = -29.845130209103
x67 = -29.845130209103