Sr Examen

Otras calculadoras

2*cos(x)/2=1-cos(x) 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]
2*cos(x)             
-------- = 1 - cos(x)
   2                 
$$\frac{2 \cos{\left(x \right)}}{2} = 1 - \cos{\left(x \right)}$$
Solución detallada
Tenemos la ecuación
$$\frac{2 \cos{\left(x \right)}}{2} = 1 - \cos{\left(x \right)}$$
es la ecuación trigonométrica más simple
Dividamos ambos miembros de la ecuación en 2

La ecuación se convierte en
$$\cos{\left(x \right)} = \frac{1}{2}$$
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
O
$$x = \pi n + \frac{\pi}{3}$$
$$x = \pi n - \frac{2 \pi}{3}$$
, donde n es cualquier número entero
Gráfica
Suma y producto de raíces [src]
suma
pi   5*pi
-- + ----
3     3  
$$\frac{\pi}{3} + \frac{5 \pi}{3}$$
=
2*pi
$$2 \pi$$
producto
pi 5*pi
--*----
3   3  
$$\frac{\pi}{3} \frac{5 \pi}{3}$$
=
    2
5*pi 
-----
  9  
$$\frac{5 \pi^{2}}{9}$$
5*pi^2/9
Respuesta rápida [src]
     pi
x1 = --
     3 
$$x_{1} = \frac{\pi}{3}$$
     5*pi
x2 = ----
      3  
$$x_{2} = \frac{5 \pi}{3}$$
x2 = 5*pi/3
Respuesta numérica [src]
x1 = 30.3687289847013
x2 = 70.162235930172
x3 = -86.9173967493176
x4 = 89.0117918517108
x5 = -17.8023583703422
x6 = 95.2949771588904
x7 = 82.7286065445312
x8 = 36.6519142918809
x9 = 55.5014702134197
x10 = 76.4454212373516
x11 = 7.33038285837618
x12 = -359.188760060433
x13 = 32.4631240870945
x14 = 38.7463093942741
x15 = 74.3510261349584
x16 = -51.3126800086333
x17 = -45.0294947014537
x18 = 99.4837673636768
x19 = -5.23598775598299
x20 = -42.9350995990605
x21 = -19.8967534727354
x22 = -13.6135681655558
x23 = 61.7846555205993
x24 = -30.3687289847013
x25 = -225.147473507269
x26 = 93.2005820564972
x27 = 11.5191730631626
x28 = 80.634211442138
x29 = -38.7463093942741
x30 = 57.5958653158129
x31 = -76.4454212373516
x32 = -95.2949771588904
x33 = -57.5958653158129
x34 = 24.0855436775217
x35 = 13.6135681655558
x36 = 5.23598775598299
x37 = -32.4631240870945
x38 = -63.8790506229925
x39 = 1651.43053823704
x40 = -26.1799387799149
x41 = 19.8967534727354
x42 = -70.162235930172
x43 = -99.4837673636768
x44 = -93.2005820564972
x45 = -49.2182849062401
x46 = -24.0855436775217
x47 = -55.5014702134197
x48 = 17.8023583703422
x49 = 63.8790506229925
x50 = -74.3510261349584
x51 = -7.33038285837618
x52 = 49.2182849062401
x53 = -89.0117918517108
x54 = -68.0678408277789
x55 = -82.7286065445312
x56 = 1.0471975511966
x57 = 51.3126800086333
x58 = -61.7846555205993
x59 = -36.6519142918809
x60 = -80.634211442138
x61 = -1.0471975511966
x62 = -11.5191730631626
x63 = 68.0678408277789
x64 = 86.9173967493176
x65 = 45.0294947014537
x66 = 26.1799387799149
x67 = 42.9350995990605
x67 = 42.9350995990605