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cosx/2=sinи la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
cos(x)         
------ = sin(I)
  2            
$$\frac{\cos{\left(x \right)}}{2} = \sin{\left(i \right)}$$
Solución detallada
Tenemos la ecuación
$$\frac{\cos{\left(x \right)}}{2} = \sin{\left(i \right)}$$
es la ecuación trigonométrica más simple
Dividamos ambos miembros de la ecuación en 1/2

La ecuación se convierte en
$$\cos{\left(x \right)} = 2 i \sinh{\left(1 \right)}$$
Como el miembro derecho de la ecuación
en el módulo =
True

pero cos
no puede ser más de 1 o menos de -1
significa que la ecuación correspondiente no tiene solución.
Gráfica
Suma y producto de raíces [src]
suma
pi                        3*pi                     
-- - I*asinh(2*sinh(1)) + ---- + I*asinh(2*sinh(1))
2                          2                       
$$\left(\frac{\pi}{2} - i \operatorname{asinh}{\left(2 \sinh{\left(1 \right)} \right)}\right) + \left(\frac{3 \pi}{2} + i \operatorname{asinh}{\left(2 \sinh{\left(1 \right)} \right)}\right)$$
=
2*pi
$$2 \pi$$
producto
/pi                     \ /3*pi                     \
|-- - I*asinh(2*sinh(1))|*|---- + I*asinh(2*sinh(1))|
\2                      / \ 2                       /
$$\left(\frac{\pi}{2} - i \operatorname{asinh}{\left(2 \sinh{\left(1 \right)} \right)}\right) \left(\frac{3 \pi}{2} + i \operatorname{asinh}{\left(2 \sinh{\left(1 \right)} \right)}\right)$$
=
                        2                        
     2              3*pi                         
asinh (2*sinh(1)) + ----- - pi*I*asinh(2*sinh(1))
                      4                          
$$\operatorname{asinh}^{2}{\left(2 \sinh{\left(1 \right)} \right)} + \frac{3 \pi^{2}}{4} - i \pi \operatorname{asinh}{\left(2 \sinh{\left(1 \right)} \right)}$$
asinh(2*sinh(1))^2 + 3*pi^2/4 - pi*i*asinh(2*sinh(1))
Respuesta rápida [src]
     pi                     
x1 = -- - I*asinh(2*sinh(1))
     2                      
$$x_{1} = \frac{\pi}{2} - i \operatorname{asinh}{\left(2 \sinh{\left(1 \right)} \right)}$$
     3*pi                     
x2 = ---- + I*asinh(2*sinh(1))
      2                       
$$x_{2} = \frac{3 \pi}{2} + i \operatorname{asinh}{\left(2 \sinh{\left(1 \right)} \right)}$$
x2 = 3*pi/2 + i*asinh(2*sinh(1))
Respuesta numérica [src]
x1 = 98.9601685880785 + 1.59019213660123*i
x2 = -45.553093477052 + 1.59019213660123*i
x3 = 83.2522053201295 - 1.59019213660123*i
x4 = -48.6946861306418 - 1.59019213660123*i
x5 = 39.2699081698724 - 1.59019213660123*i
x6 = 67.5442420521806 + 1.59019213660123*i
x7 = -92.6769832808989 - 1.59019213660123*i
x8 = 42.4115008234622 + 1.59019213660123*i
x9 = -7.85398163397448 + 1.59019213660123*i
x10 = -42.4115008234622 - 1.59019213660123*i
x11 = -61.261056745001 - 1.59019213660123*i
x12 = 73.8274273593601 + 1.59019213660123*i
x13 = 23.5619449019235 + 1.59019213660123*i
x14 = -76.9690200129499 + 1.59019213660123*i
x15 = 54.9778714378214 + 1.59019213660123*i
x16 = 80.1106126665397 + 1.59019213660123*i
x17 = -51.8362787842316 + 1.59019213660123*i
x18 = -39.2699081698724 + 1.59019213660123*i
x19 = 45.553093477052 - 1.59019213660123*i
x20 = -80.1106126665397 - 1.59019213660123*i
x21 = -54.9778714378214 - 1.59019213660123*i
x22 = -83.2522053201295 + 1.59019213660123*i
x23 = 86.3937979737193 + 1.59019213660123*i
x24 = -58.1194640914112 + 1.59019213660123*i
x25 = -36.1283155162826 - 1.59019213660123*i
x26 = -64.4026493985908 + 1.59019213660123*i
x27 = 29.845130209103 + 1.59019213660123*i
x28 = -4.71238898038469 - 1.59019213660123*i
x29 = 10.9955742875643 + 1.59019213660123*i
x30 = -89.5353906273091 + 1.59019213660123*i
x31 = 64.4026493985908 - 1.59019213660123*i
x32 = 61.261056745001 + 1.59019213660123*i
x33 = -26.7035375555132 + 1.59019213660123*i
x34 = -1.5707963267949 + 1.59019213660123*i
x35 = 70.6858347057703 - 1.59019213660123*i
x36 = -14.1371669411541 + 1.59019213660123*i
x37 = -17.2787595947439 - 1.59019213660123*i
x38 = -86.3937979737193 - 1.59019213660123*i
x39 = 95.8185759344887 - 1.59019213660123*i
x40 = 48.6946861306418 + 1.59019213660123*i
x41 = -95.8185759344887 + 1.59019213660123*i
x42 = -10.9955742875643 - 1.59019213660123*i
x43 = 51.8362787842316 - 1.59019213660123*i
x44 = -29.845130209103 - 1.59019213660123*i
x45 = -67.5442420521806 - 1.59019213660123*i
x46 = -23.5619449019235 - 1.59019213660123*i
x47 = -70.6858347057703 + 1.59019213660123*i
x48 = -73.8274273593601 - 1.59019213660123*i
x49 = 92.6769832808989 + 1.59019213660123*i
x50 = 36.1283155162826 + 1.59019213660123*i
x51 = -20.4203522483337 + 1.59019213660123*i
x52 = 7.85398163397448 - 1.59019213660123*i
x53 = -98.9601685880785 - 1.59019213660123*i
x54 = 76.9690200129499 - 1.59019213660123*i
x55 = 4.71238898038469 + 1.59019213660123*i
x56 = 1.5707963267949 - 1.59019213660123*i
x57 = -32.9867228626928 + 1.59019213660123*i
x58 = 58.1194640914112 - 1.59019213660123*i
x59 = 32.9867228626928 - 1.59019213660123*i
x60 = 17.2787595947439 + 1.59019213660123*i
x61 = 89.5353906273091 - 1.59019213660123*i
x62 = 14.1371669411541 - 1.59019213660123*i
x63 = 20.4203522483337 - 1.59019213660123*i
x64 = 26.7035375555132 - 1.59019213660123*i
x64 = 26.7035375555132 - 1.59019213660123*i