Sr Examen

Otras calculadoras

cos^3x 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] 
   3       
cos (x) = 0
cos⁡3(x)=0\cos^{3}{\left(x \right)} = 0
Simplificar
Solución detallada
Tenemos la ecuación
cos⁡3(x)=0\cos^{3}{\left(x \right)} = 0
cambiamos
cos⁡3(x)=0\cos^{3}{\left(x \right)} = 0
cos⁡3(x)=0\cos^{3}{\left(x \right)} = 0
Sustituimos
w=cos⁡(x)w = \cos{\left(x \right)}
Tenemos la ecuación
w3=0w^{3} = 0
es decir
w=0w = 0
Obtenemos la respuesta: w = 0
hacemos cambio inverso
cos⁡(x)=w\cos{\left(x \right)} = w
Tenemos la ecuación
cos⁡(x)=w\cos{\left(x \right)} = w
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
x=πn+acos⁡(w)x = \pi n + \operatorname{acos}{\left(w \right)}
x=πn+acos⁡(w)−πx = \pi n + \operatorname{acos}{\left(w \right)} - \pi
O
x=πn+acos⁡(w)x = \pi n + \operatorname{acos}{\left(w \right)}
x=πn+acos⁡(w)−πx = \pi n + \operatorname{acos}{\left(w \right)} - \pi
, donde n es cualquier número entero
sustituimos w:
x1=πn+acos⁡(w1)x_{1} = \pi n + \operatorname{acos}{\left(w_{1} \right)}
x1=πn+acos⁡(0)x_{1} = \pi n + \operatorname{acos}{\left(0 \right)}
x1=πn+π2x_{1} = \pi n + \frac{\pi}{2}
x2=πn+acos⁡(w1)−πx_{2} = \pi n + \operatorname{acos}{\left(w_{1} \right)} - \pi
x2=πn−π+acos⁡(0)x_{2} = \pi n - \pi + \operatorname{acos}{\left(0 \right)}
x2=πn−π2x_{2} = \pi n - \frac{\pi}{2}
Gráfica
0-80-60-40-2020406080-1001002-2
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
pi   3*pi
-- + ----
2     2
π2+3π2\frac{\pi}{2} + \frac{3 \pi}{2} 
=
2*pi
2π2 \pi 
producto
pi 3*pi
--*----
2   2
π23π2\frac{\pi}{2} \frac{3 \pi}{2} 
=
    2
3*pi 
-----
  4
3π24\frac{3 \pi^{2}}{4} 
3*pi^2/4
Respuesta rápida [src] 
     pi
x1 = --
     2
x1=π2x_{1} = \frac{\pi}{2} 
     3*pi
x2 = ----
      2
x2=3π2x_{2} = \frac{3 \pi}{2} 
x2 = 3*pi/2
Respuesta numérica [src] 
x1 = -73.827410994311
x2 = 42.4114617473496
x3 = 45.5531567451367
x4 = 20.4203112367381
x5 = 23.5619763533234
x6 = 29.8451754771722
x7 = -14.1371260033657
x8 = 70.6858302611407
x9 = -89.5354410428862
x10 = 73.8274768053124
x11 = 58.1194603256925
x12 = 70.6857435758276
x13 = 95.818627417042
x14 = -17.2788562472482
x15 = 92.6768935770301
x16 = -23.5619897288019
x17 = 67.5443333859623
x18 = -80.1105785507599
x19 = -29.8451152214988
x20 = 45.553194340988
x21 = -67.5442906223714
x22 = 48.6945935926021
x23 = -64.4025554047934
x24 = -83.2523004207065
x25 = -45.5531401844306
x26 = 67.5443442271897
x27 = 26.7034436275456
x28 = 89.5354940921686
x29 = -83.2523059178598
x30 = -39.2700061565569
x31 = 92.6770059000324
x32 = 26.7034598912501
x33 = 36.128317789764
x34 = 80.1106035284868
x35 = -58.1194276545353
x36 = 14.1371748405436
x37 = 4.71228651848371
x38 = -61.2611560468397
x39 = 7.85402475701276
x40 = 23.5620444336803
x41 = -1.57083925518957
x42 = -95.8185603030962
x43 = 1.57080273224359
x44 = -92.6770895717702
x45 = 4.71229368085888
x46 = -61.2611644481175
x47 = -51.8362625267018
x48 = 51.8363261592826
x49 = -42.4114638604687
x50 = -20.4202554438585
x51 = -7.85396939058216
x52 = 64.4026122770508
x53 = -36.1282768063468
x54 = -86.3937054164085
x55 = -20.4203505482106
x56 = -42.411405413931
x57 = 48.6946439323886
x58 = 86.3937628262857
x59 = 1.5708945053691
x59 = 1.5708945053691
    © Sr Examen – Калькулятор