Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación 8*x=2
-
Ecuación 3^x=81
-
Ecuación 5x+15=x-1
-
Ecuación 2*x^2-x+5=0
- Expresar {x} en función de y en la ecuación:
- 4*x-1*y=-3
- -11*x+9*y=-20
- 9*x+17*y=13
- -17*x+2*y=9
- Derivada de:
-
cosx
- Integral de d{x}:
- cosx
- Gráfico de la función y =:
-
cosx
-
Expresiones idénticas
- cosx=(3i)/ cuatro
- coseno de x es igual a (3i) dividir por 4
- coseno de x es igual a (3i) dividir por cuatro
- cosx=3i/4
- cosx=(3i) dividir por 4
-
Expresiones semejantes
- x^2=cos(x)
- sin(z)=3i/4
- 2*sin(x)-3*cos(x)=0
- 2*cos(x)=1
- sin(x)+cos(x)=1-sin(2*x)
- 1-cos(x)=sin(x/2)
-
Expresiones con funciones
- cosx
- cosx(x^2+x+1)=y
- cosx+v3*(1-sinx)=0
- cosx=p/2
- cosx+sinx=1/(2)^1/2
- cosx-0,5x+1=0
cosx=(3i)/4 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\cos{\left(x \right)} = \frac{3 i}{4}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{acos}{\left(\frac{3 i}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{3 i}{4} \right)}$$
O
$$x = \pi n + \frac{\pi}{2} - i \operatorname{asinh}{\left(\frac{3}{4} \right)}$$
$$x = \pi n - \frac{\pi}{2} - i \operatorname{asinh}{\left(\frac{3}{4} \right)}$$
, donde n es cualquier número entero
$$\cos{\left(x \right)} = \frac{3 i}{4}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{acos}{\left(\frac{3 i}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{3 i}{4} \right)}$$
O
$$x = \pi n + \frac{\pi}{2} - i \operatorname{asinh}{\left(\frac{3}{4} \right)}$$
$$x = \pi n - \frac{\pi}{2} - i \operatorname{asinh}{\left(\frac{3}{4} \right)}$$
, donde n es cualquier número entero
Gráfica
Respuesta rápida
[src]
pi
x1 = -- - I*asinh(3/4)
2
$$x_{1} = \frac{\pi}{2} - i \operatorname{asinh}{\left(\frac{3}{4} \right)}$$
3*pi
x2 = ---- + I*asinh(3/4)
2
$$x_{2} = \frac{3 \pi}{2} + i \operatorname{asinh}{\left(\frac{3}{4} \right)}$$
x2 = 3*pi/2 + i*asinh(3/4)
Suma y producto de raíces
[src]
suma
pi 3*pi -- - I*asinh(3/4) + ---- + I*asinh(3/4) 2 2
$$\left(\frac{\pi}{2} - i \operatorname{asinh}{\left(\frac{3}{4} \right)}\right) + \left(\frac{3 \pi}{2} + i \operatorname{asinh}{\left(\frac{3}{4} \right)}\right)$$
=
2*pi
$$2 \pi$$
producto
/pi \ /3*pi \ |-- - I*asinh(3/4)|*|---- + I*asinh(3/4)| \2 / \ 2 /
$$\left(\frac{\pi}{2} - i \operatorname{asinh}{\left(\frac{3}{4} \right)}\right) \left(\frac{3 \pi}{2} + i \operatorname{asinh}{\left(\frac{3}{4} \right)}\right)$$
=
2
2 3*pi
asinh (3/4) + ----- - pi*I*asinh(3/4)
4
$$\operatorname{asinh}^{2}{\left(\frac{3}{4} \right)} + \frac{3 \pi^{2}}{4} - i \pi \operatorname{asinh}{\left(\frac{3}{4} \right)}$$
asinh(3/4)^2 + 3*pi^2/4 - pi*i*asinh(3/4)
Respuesta numérica
[src]
x1 = -80.1106126665397 - 0.693147180559945*i
x2 = -70.6858347057703 + 0.693147180559945*i
x3 = -42.4115008234622 - 0.693147180559945*i
x4 = 29.845130209103 + 0.693147180559945*i
x5 = -54.9778714378214 - 0.693147180559945*i
x6 = 14.1371669411541 - 0.693147180559945*i
x7 = 95.8185759344887 - 0.693147180559945*i
x8 = -39.2699081698724 + 0.693147180559945*i
x9 = 20.4203522483337 - 0.693147180559945*i
x10 = -48.6946861306418 - 0.693147180559945*i
x11 = 70.6858347057703 - 0.693147180559945*i
x12 = -10.9955742875643 - 0.693147180559945*i
x13 = 10.9955742875643 + 0.693147180559945*i
x14 = 67.5442420521806 + 0.693147180559945*i
x15 = -58.1194640914112 + 0.693147180559945*i
x16 = -86.3937979737193 - 0.693147180559945*i
x17 = -32.9867228626928 + 0.693147180559945*i
x18 = -98.9601685880785 - 0.693147180559945*i
x19 = 83.2522053201295 - 0.693147180559945*i
x20 = 4.71238898038469 + 0.693147180559945*i
x21 = 80.1106126665397 + 0.693147180559945*i
x22 = 39.2699081698724 - 0.693147180559945*i
x23 = 92.6769832808989 + 0.693147180559945*i
x24 = 51.8362787842316 - 0.693147180559945*i
x25 = -73.8274273593601 - 0.693147180559945*i
x26 = -76.9690200129499 + 0.693147180559945*i
x27 = 76.9690200129499 - 0.693147180559945*i
x28 = 45.553093477052 - 0.693147180559945*i
x29 = -45.553093477052 + 0.693147180559945*i
x30 = 36.1283155162826 + 0.693147180559945*i
x31 = 42.4115008234622 + 0.693147180559945*i
x32 = 1.5707963267949 - 0.693147180559945*i
x33 = -1.5707963267949 + 0.693147180559945*i
x34 = 58.1194640914112 - 0.693147180559945*i
x35 = 86.3937979737193 + 0.693147180559945*i
x36 = -7.85398163397448 + 0.693147180559945*i
x37 = 54.9778714378214 + 0.693147180559945*i
x38 = 7.85398163397448 - 0.693147180559945*i
x39 = -36.1283155162826 - 0.693147180559945*i
x40 = -64.4026493985908 + 0.693147180559945*i
x41 = -95.8185759344887 + 0.693147180559945*i
x42 = -23.5619449019235 - 0.693147180559945*i
x43 = 89.5353906273091 - 0.693147180559945*i
x44 = -14.1371669411541 + 0.693147180559945*i
x45 = -20.4203522483337 + 0.693147180559945*i
x46 = 48.6946861306418 + 0.693147180559945*i
x47 = 73.8274273593601 + 0.693147180559945*i
x48 = 17.2787595947439 + 0.693147180559945*i
x49 = 26.7035375555132 - 0.693147180559945*i
x50 = 32.9867228626928 - 0.693147180559945*i
x51 = -67.5442420521806 - 0.693147180559945*i
x52 = 64.4026493985908 - 0.693147180559945*i
x53 = -17.2787595947439 - 0.693147180559945*i
x54 = -61.261056745001 - 0.693147180559945*i
x55 = 23.5619449019235 + 0.693147180559945*i
x56 = -51.8362787842316 + 0.693147180559945*i
x57 = -29.845130209103 - 0.693147180559945*i
x58 = -83.2522053201295 + 0.693147180559945*i
x59 = 61.261056745001 + 0.693147180559945*i
x60 = -26.7035375555132 + 0.693147180559945*i
x61 = -92.6769832808989 - 0.693147180559945*i
x62 = -4.71238898038469 - 0.693147180559945*i
x63 = -89.5353906273091 + 0.693147180559945*i
x64 = 98.9601685880785 + 0.693147180559945*i
x64 = 98.9601685880785 + 0.693147180559945*i