Sr Examen

Otras calculadoras

sin*(pi(*5x+15)/6)=1/2 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
   /pi*(5*x + 15)\      
sin|-------------| = 1/2
   \      6      /      
$$\sin{\left(\frac{\pi \left(5 x + 15\right)}{6} \right)} = \frac{1}{2}$$
Solución detallada
Tenemos la ecuación
$$\sin{\left(\frac{\pi \left(5 x + 15\right)}{6} \right)} = \frac{1}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$\frac{5 \pi x}{6} = \pi n + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
$$\frac{5 \pi x}{6} = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
O
$$\frac{5 \pi x}{6} = \pi n + \frac{\pi}{3}$$
$$\frac{5 \pi x}{6} = \pi n - \frac{2 \pi}{3}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$\frac{5 \pi}{6}$$
obtenemos la respuesta:
$$x_{1} = \frac{6 \left(\pi n + \frac{\pi}{3}\right)}{5 \pi}$$
$$x_{2} = \frac{6 \left(\pi n - \frac{2 \pi}{3}\right)}{5 \pi}$$
Gráfica
Respuesta rápida [src]
x1 = 2/5
$$x_{1} = \frac{2}{5}$$
x2 = 2
$$x_{2} = 2$$
x2 = 2
Suma y producto de raíces [src]
suma
2 + 2/5
$$\frac{2}{5} + 2$$
=
12/5
$$\frac{12}{5}$$
producto
2*2
---
 5 
$$\frac{2 \cdot 2}{5}$$
=
4/5
$$\frac{4}{5}$$
4/5
Respuesta numérica [src]
x1 = -34.0
x2 = -88.4
x3 = 0.4
x4 = -46.0
x5 = 28.4
x6 = 134.8
x7 = 96.4
x8 = -74.0
x9 = 76.4
x10 = 170.8
x11 = -10.0
x12 = -7.6
x13 = 19.6
x14 = 38.8
x15 = -94.0
x16 = 62.0
x17 = -26.0
x18 = 50.0
x19 = 14.0
x20 = 67.6
x21 = -23.6
x22 = 60.4
x23 = -55.6
x24 = -28.4
x25 = 84.4
x26 = -4.4
x27 = -59.6
x28 = 74.8
x29 = -31.6
x30 = 206.8
x31 = -64.4
x32 = 55.6
x33 = 34.0
x34 = 218.8
x35 = 91.6
x36 = -86.0
x37 = -19.6
x38 = 50.8
x39 = 58.0
x40 = -79.6
x41 = 74.0
x42 = 2.0
x43 = -40.4
x44 = -22.0
x45 = 70.0
x46 = -11.6
x47 = -43.6
x48 = 43.6
x49 = 4.4
x50 = 12.4
x51 = 158.8
x52 = 10.0
x53 = -98.0
x54 = -83.6
x55 = -95.6
x56 = -62.0
x57 = 122.8
x58 = -76.4
x59 = -71.6
x60 = 16.4
x61 = 40.4
x62 = 36.4
x63 = 72.4
x64 = 82.0
x65 = 62.8
x66 = -35.6
x67 = -58.0
x68 = 146.8
x69 = 22.0
x70 = -70.0
x71 = 86.8
x72 = -52.4
x73 = 46.0
x74 = 110.8
x75 = 26.0
x76 = -82.0
x77 = -50.0
x78 = 182.8
x79 = 52.4
x80 = 86.0
x81 = 38.0
x82 = 64.4
x83 = 31.6
x84 = 100.4
x85 = -14.0
x86 = 94.0
x87 = 98.8
x88 = 98.0
x89 = 194.8
x90 = -47.6
x91 = 7.6
x92 = 48.4
x93 = -100.4
x94 = -67.6
x95 = 88.4
x96 = 24.4
x97 = 79.6
x98 = -91.6
x99 = -38.0
x100 = -16.4
x101 = -2.0
x101 = -2.0