Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación 8*x-3*(2*x+1)=2*x+4
-
Ecuación x^3=27
-
Ecuación 1+sin(x)=0
-
Ecuación 2*x^2+6*x+9=
- Expresar {x} en función de y en la ecuación:
- 20*x+6*y=8
- -11*x-15*y=14
- -11*x+10*y=-9
- 6*x-2*y=20
- Límite de la función:
- pi*sin(pi*x)
-
Expresiones idénticas
- pi*sin(pi*x)= uno
- número pi multiplicar por seno de ( número pi multiplicar por x) es igual a 1
- número pi multiplicar por seno de ( número pi multiplicar por x) es igual a uno
- pisin(pix)=1
- pisinpix=1
-
Expresiones con funciones
- Número Pi pi
- pi*pi*x=3*f*(x)
- pi-arccosx=0
- pi/3=2*x-pi/4
- pi(x+2)/12=(1/2)
- pi^x=x
- Seno sin
- sin(x-pi/3)=0
- sin(x/2)=1/2
- sin^24𝑥−sin4𝑥−2=0
- sin(2*x)=-1/2
- sin(pi*x)=-1
- Número Pi pi
- pi*pi*x=3*f*(x)
- pi-arccosx=0
- pi/3=2*x-pi/4
- pi(x+2)/12=(1/2)
- pi^x=x
pi*sin(pi*x)=1 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\pi \sin{\left(\pi x \right)} = 1$$
es la ecuación trigonométrica más simple
La ecuación se convierte en
$$\sin{\left(\pi x \right)} = \frac{1}{\pi}$$
Esta ecuación se reorganiza en
$$\pi x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{\pi} \right)}$$
$$\pi x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{\pi} \right)} + \pi$$
O
$$\pi x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{\pi} \right)}$$
$$\pi x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{\pi} \right)} + \pi$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$\pi$$
obtenemos la respuesta:
$$x_{1} = \frac{2 \pi n + \operatorname{asin}{\left(\frac{1}{\pi} \right)}}{\pi}$$
$$x_{2} = \frac{2 \pi n - \operatorname{asin}{\left(\frac{1}{\pi} \right)} + \pi}{\pi}$$
$$\pi \sin{\left(\pi x \right)} = 1$$
es la ecuación trigonométrica más simple
Dividamos ambos miembros de la ecuación en pi
La ecuación se convierte en
$$\sin{\left(\pi x \right)} = \frac{1}{\pi}$$
Esta ecuación se reorganiza en
$$\pi x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{\pi} \right)}$$
$$\pi x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{\pi} \right)} + \pi$$
O
$$\pi x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{\pi} \right)}$$
$$\pi x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{\pi} \right)} + \pi$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$\pi$$
obtenemos la respuesta:
$$x_{1} = \frac{2 \pi n + \operatorname{asin}{\left(\frac{1}{\pi} \right)}}{\pi}$$
$$x_{2} = \frac{2 \pi n - \operatorname{asin}{\left(\frac{1}{\pi} \right)} + \pi}{\pi}$$
Respuesta rápida
[src]
/1 \
pi - asin|--|
\pi/
x1 = -------------
pi
$$x_{1} = \frac{\pi - \operatorname{asin}{\left(\frac{1}{\pi} \right)}}{\pi}$$
/1 \
asin|--|
\pi/
x2 = --------
pi
$$x_{2} = \frac{\operatorname{asin}{\left(\frac{1}{\pi} \right)}}{\pi}$$
x2 = asin(1/pi)/pi
Suma y producto de raíces
[src]
suma
/1 \ /1 \
pi - asin|--| asin|--|
\pi/ \pi/
------------- + --------
pi pi
$$\frac{\operatorname{asin}{\left(\frac{1}{\pi} \right)}}{\pi} + \frac{\pi - \operatorname{asin}{\left(\frac{1}{\pi} \right)}}{\pi}$$
=
/1 \ /1 \
pi - asin|--| asin|--|
\pi/ \pi/
------------- + --------
pi pi
$$\frac{\operatorname{asin}{\left(\frac{1}{\pi} \right)}}{\pi} + \frac{\pi - \operatorname{asin}{\left(\frac{1}{\pi} \right)}}{\pi}$$
producto
/1 \ /1 \
pi - asin|--| asin|--|
\pi/ \pi/
-------------*--------
pi pi
$$\frac{\pi - \operatorname{asin}{\left(\frac{1}{\pi} \right)}}{\pi} \frac{\operatorname{asin}{\left(\frac{1}{\pi} \right)}}{\pi}$$
=
/ /1 \\ /1 \
|pi - asin|--||*asin|--|
\ \pi// \pi/
------------------------
2
pi
$$\frac{\left(\pi - \operatorname{asin}{\left(\frac{1}{\pi} \right)}\right) \operatorname{asin}{\left(\frac{1}{\pi} \right)}}{\pi^{2}}$$
(pi - asin(1/pi))*asin(1/pi)/pi^2
Respuesta numérica
[src]
x1 = 62.1031152484272
x2 = 80.1031152484272
x3 = 16.1031152484272
x4 = -69.8968847515728
x5 = -41.8968847515728
x6 = -81.8968847515728
x7 = 46.1031152484272
x8 = 34.1031152484272
x9 = 86.1031152484272
x10 = 66.1031152484272
x11 = -65.8968847515728
x12 = 70.1031152484272
x13 = 8.1031152484272
x14 = -63.8968847515728
x15 = -27.8968847515728
x16 = -73.8968847515728
x17 = 98.1031152484272
x18 = 94.1031152484272
x19 = 74.1031152484272
x20 = 96.1031152484272
x21 = -25.8968847515728
x22 = 18.1031152484272
x23 = 56.1031152484272
x24 = -47.8968847515728
x25 = 12.1031152484272
x26 = -87.8968847515728
x27 = 54.1031152484272
x28 = 84.1031152484272
x29 = -57.8968847515728
x30 = 64.1031152484272
x31 = -89.8968847515728
x32 = -23.8968847515728
x33 = -77.8968847515728
x34 = -35.8968847515728
x35 = -17.8968847515728
x36 = -39.8968847515728
x37 = -71.8968847515728
x38 = -29.8968847515728
x39 = 30.1031152484272
x40 = 38.1031152484272
x41 = 52.1031152484272
x42 = 28.1031152484272
x43 = -51.8968847515728
x44 = 90.1031152484272
x45 = -15.8968847515728
x46 = -97.8968847515728
x47 = 32.1031152484272
x48 = 22.1031152484272
x49 = 0.103115248427201
x50 = -55.8968847515728
x51 = -91.8968847515728
x52 = -53.8968847515728
x53 = 2.1031152484272
x54 = -13.8968847515728
x55 = 58.1031152484272
x56 = 68.1031152484272
x57 = 100.103115248427
x58 = 20.1031152484272
x59 = -75.8968847515728
x60 = -95.8968847515728
x61 = -59.8968847515728
x62 = -93.8968847515728
x63 = -43.8968847515728
x64 = 4.1031152484272
x65 = 36.1031152484272
x66 = -5.8968847515728
x67 = 44.1031152484272
x68 = -79.8968847515728
x69 = 72.1031152484272
x70 = 6.1031152484272
x71 = -9.8968847515728
x72 = 42.1031152484272
x73 = -33.8968847515728
x74 = 76.1031152484272
x75 = 88.1031152484272
x76 = 48.1031152484272
x77 = 14.1031152484272
x78 = -37.8968847515728
x79 = 24.1031152484272
x80 = 82.1031152484272
x81 = -99.8968847515728
x82 = -85.8968847515728
x83 = -83.8968847515728
x84 = 92.1031152484272
x85 = -49.8968847515728
x86 = -21.8968847515728
x87 = -61.8968847515728
x88 = -11.8968847515728
x89 = -3.8968847515728
x90 = 60.1031152484272
x91 = -45.8968847515728
x92 = -19.8968847515728
x93 = 40.1031152484272
x94 = -7.8968847515728
x95 = -31.8968847515728
x96 = 78.1031152484272
x97 = 50.1031152484272
x98 = 10.1031152484272
x99 = -1.8968847515728
x100 = -67.8968847515728
x101 = 26.1031152484272
x101 = 26.1031152484272