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- La ecuación:
-
Ecuación x^2+2x-4=0
-
Ecuación x²-25=0
-
Ecuación x^4-2*x^2=0
-
Ecuación x^3+3x^2=0
- Expresar {x} en función de y en la ecuación:
- 14*x-18*y=5
- -5*x+2*y=-14
- 1*x-5*y=-17
- 4*x+3*y=-15
- Límite de la función:
- cos(z)
- Gráfico de la función y =:
-
cos(z)
- Integral de d{x}:
- cos(z)
-
Expresiones idénticas
- cos(z)=(sqrt(tres)/ dos)*i
- coseno de (z) es igual a ( raíz cuadrada de (3) dividir por 2) multiplicar por i
- coseno de (z) es igual a ( raíz cuadrada de (tres) dividir por dos) multiplicar por i
- cos(z)=(√(3)/2)*i
- cos(z)=(sqrt(3)/2)i
- cosz=sqrt3/2i
- cos(z)=(sqrt(3) dividir por 2)*i
-
Expresiones semejantes
- cos(z+i)=(-3/4)*i
- isinz+cosz=i
- z^4+1/2+(sqrt(3)/2)i=0
- cosz=2
-
Expresiones con funciones
- Coseno cos
- cos2x*sin3x-sin2x*cos3x=1
- cos(x)=-(1/2)
- cos(x)=(4/5)
- cos2x=0
- cos(x)=2/3
- Raíz cuadrada sqrt
- sqrt(2)*sin(x)=1
- sqrt(4x-1)=y
- sqrt(x+4+2sqrt(x+3))+sqrt(x+4-2sqrt(x+3))=2
- sqrt(x^2-64)+sqrt(x^2-36)=28/(x-8)
- sqrt(3x+7)=x-7
cos(z)=(sqrt(3)/2)*i la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\cos{\left(z \right)} = i \frac{\sqrt{3}}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$z = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3} i}{2} \right)}$$
$$z = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3} i}{2} \right)}$$
O
$$z = \pi n + \frac{\pi}{2} - i \operatorname{asinh}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$z = \pi n - \frac{\pi}{2} - i \operatorname{asinh}{\left(\frac{\sqrt{3}}{2} \right)}$$
, donde n es cualquier número entero
$$\cos{\left(z \right)} = i \frac{\sqrt{3}}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$z = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3} i}{2} \right)}$$
$$z = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3} i}{2} \right)}$$
O
$$z = \pi n + \frac{\pi}{2} - i \operatorname{asinh}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$z = \pi n - \frac{\pi}{2} - i \operatorname{asinh}{\left(\frac{\sqrt{3}}{2} \right)}$$
, donde n es cualquier número entero
Gráfica
Respuesta rápida
[src]
/ ___\
pi |\/ 3 |
z1 = -- - I*asinh|-----|
2 \ 2 /
$$z_{1} = \frac{\pi}{2} - i \operatorname{asinh}{\left(\frac{\sqrt{3}}{2} \right)}$$
/ ___\
3*pi |\/ 3 |
z2 = ---- + I*asinh|-----|
2 \ 2 /
$$z_{2} = \frac{3 \pi}{2} + i \operatorname{asinh}{\left(\frac{\sqrt{3}}{2} \right)}$$
z2 = 3*pi/2 + i*asinh(sqrt(3)/2)
Suma y producto de raíces
[src]
suma
/ ___\ / ___\ pi |\/ 3 | 3*pi |\/ 3 | -- - I*asinh|-----| + ---- + I*asinh|-----| 2 \ 2 / 2 \ 2 /
$$\left(\frac{\pi}{2} - i \operatorname{asinh}{\left(\frac{\sqrt{3}}{2} \right)}\right) + \left(\frac{3 \pi}{2} + i \operatorname{asinh}{\left(\frac{\sqrt{3}}{2} \right)}\right)$$
=
2*pi
$$2 \pi$$
producto
/ / ___\\ / / ___\\ |pi |\/ 3 || |3*pi |\/ 3 || |-- - I*asinh|-----||*|---- + I*asinh|-----|| \2 \ 2 // \ 2 \ 2 //
$$\left(\frac{\pi}{2} - i \operatorname{asinh}{\left(\frac{\sqrt{3}}{2} \right)}\right) \left(\frac{3 \pi}{2} + i \operatorname{asinh}{\left(\frac{\sqrt{3}}{2} \right)}\right)$$
=
/ ___\ 2 / ___\
2|\/ 3 | 3*pi |\/ 3 |
asinh |-----| + ----- - pi*I*asinh|-----|
\ 2 / 4 \ 2 /
$$\operatorname{asinh}^{2}{\left(\frac{\sqrt{3}}{2} \right)} + \frac{3 \pi^{2}}{4} - i \pi \operatorname{asinh}{\left(\frac{\sqrt{3}}{2} \right)}$$
asinh(sqrt(3)/2)^2 + 3*pi^2/4 - pi*i*asinh(sqrt(3)/2)
Respuesta numérica
[src]
z1 = 64.4026493985908 - 0.783399618486206*i
z2 = -51.8362787842316 + 0.783399618486206*i
z3 = 76.9690200129499 - 0.783399618486206*i
z4 = -83.2522053201295 + 0.783399618486206*i
z5 = 83.2522053201295 - 0.783399618486206*i
z6 = 4.71238898038469 + 0.783399618486206*i
z7 = 54.9778714378214 + 0.783399618486206*i
z8 = 39.2699081698724 - 0.783399618486206*i
z9 = -7.85398163397448 + 0.783399618486206*i
z10 = -17.2787595947439 - 0.783399618486206*i
z11 = 89.5353906273091 - 0.783399618486206*i
z12 = -45.553093477052 + 0.783399618486206*i
z13 = -14.1371669411541 + 0.783399618486206*i
z14 = 23.5619449019235 + 0.783399618486206*i
z15 = -54.9778714378214 - 0.783399618486206*i
z16 = 10.9955742875643 + 0.783399618486206*i
z17 = -89.5353906273091 + 0.783399618486206*i
z18 = 61.261056745001 + 0.783399618486206*i
z19 = -4.71238898038469 - 0.783399618486206*i
z20 = 73.8274273593601 + 0.783399618486206*i
z21 = -26.7035375555132 + 0.783399618486206*i
z22 = 80.1106126665397 + 0.783399618486206*i
z23 = 95.8185759344887 - 0.783399618486206*i
z24 = -58.1194640914112 + 0.783399618486206*i
z25 = -32.9867228626928 + 0.783399618486206*i
z26 = -10.9955742875643 - 0.783399618486206*i
z27 = 67.5442420521806 + 0.783399618486206*i
z28 = -80.1106126665397 - 0.783399618486206*i
z29 = -70.6858347057703 + 0.783399618486206*i
z30 = 14.1371669411541 - 0.783399618486206*i
z31 = 98.9601685880785 + 0.783399618486206*i
z32 = -98.9601685880785 - 0.783399618486206*i
z33 = -36.1283155162826 - 0.783399618486206*i
z34 = -20.4203522483337 + 0.783399618486206*i
z35 = -23.5619449019235 - 0.783399618486206*i
z36 = -86.3937979737193 - 0.783399618486206*i
z37 = -64.4026493985908 + 0.783399618486206*i
z38 = -73.8274273593601 - 0.783399618486206*i
z39 = 32.9867228626928 - 0.783399618486206*i
z40 = -42.4115008234622 - 0.783399618486206*i
z41 = -95.8185759344887 + 0.783399618486206*i
z42 = 45.553093477052 - 0.783399618486206*i
z43 = 17.2787595947439 + 0.783399618486206*i
z44 = 42.4115008234622 + 0.783399618486206*i
z45 = -61.261056745001 - 0.783399618486206*i
z46 = 1.5707963267949 - 0.783399618486206*i
z47 = 26.7035375555132 - 0.783399618486206*i
z48 = -1.5707963267949 + 0.783399618486206*i
z49 = -39.2699081698724 + 0.783399618486206*i
z50 = -76.9690200129499 + 0.783399618486206*i
z51 = 29.845130209103 + 0.783399618486206*i
z52 = 20.4203522483337 - 0.783399618486206*i
z53 = -67.5442420521806 - 0.783399618486206*i
z54 = -29.845130209103 - 0.783399618486206*i
z55 = -92.6769832808989 - 0.783399618486206*i
z56 = 86.3937979737193 + 0.783399618486206*i
z57 = 48.6946861306418 + 0.783399618486206*i
z58 = 7.85398163397448 - 0.783399618486206*i
z59 = 58.1194640914112 - 0.783399618486206*i
z60 = -48.6946861306418 - 0.783399618486206*i
z61 = 36.1283155162826 + 0.783399618486206*i
z62 = 70.6858347057703 - 0.783399618486206*i
z63 = 51.8362787842316 - 0.783399618486206*i
z64 = 92.6769832808989 + 0.783399618486206*i
z64 = 92.6769832808989 + 0.783399618486206*i