Sr Examen

Otras calculadoras

cos^-2(x)=1 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] 
   1       
------- = 1
   2       
cos (x)
1cos⁡2(x)=1\frac{1}{\cos^{2}{\left(x \right)}} = 1
Simplificar
Solución detallada
Tenemos la ecuación
1cos⁡2(x)=1\frac{1}{\cos^{2}{\left(x \right)}} = 1
cambiamos
tan⁡2(x)=0\tan^{2}{\left(x \right)} = 0
−1+1cos⁡2(x)=0-1 + \frac{1}{\cos^{2}{\left(x \right)}} = 0
Sustituimos
w=cos⁡(x)w = \cos{\left(x \right)}
Tenemos la ecuación
−1+1w2=0-1 + \frac{1}{w^{2}} = 0
Ya que la potencia en la ecuación es igual a = -2 - contiene un número par -2 en el numerador, entonces
la ecuación tendrá dos raíces reales.
Extraigamos la raíz de potencia -2 de las dos partes de la ecuación:
Obtenemos:
11w2=11\frac{1}{\sqrt{\frac{1}{w^{2}}}} = \frac{1}{\sqrt{1}}
11w2=(−1)11\frac{1}{\sqrt{\frac{1}{w^{2}}}} = \left(-1\right) \frac{1}{\sqrt{1}}
o
w=1w = 1
w=−1w = -1
Obtenemos la respuesta: w = 1
Obtenemos la respuesta: w = -1
o
w1=−1w_{1} = -1
w2=1w_{2} = 1

Entonces la respuesta definitiva es:
w1=−1w_{1} = -1
w2=1w_{2} = 1
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⁡(1)x_{1} = \pi n + \operatorname{acos}{\left(1 \right)}
x1=πnx_{1} = \pi n
x2=πn+acos⁡(w2)x_{2} = \pi n + \operatorname{acos}{\left(w_{2} \right)}
x2=πn+acos⁡(−1)x_{2} = \pi n + \operatorname{acos}{\left(-1 \right)}
x2=πn+πx_{2} = \pi n + \pi
x3=πn+acos⁡(w1)−πx_{3} = \pi n + \operatorname{acos}{\left(w_{1} \right)} - \pi
x3=πn−π+acos⁡(1)x_{3} = \pi n - \pi + \operatorname{acos}{\left(1 \right)}
x3=πn−πx_{3} = \pi n - \pi
x4=πn+acos⁡(w2)−πx_{4} = \pi n + \operatorname{acos}{\left(w_{2} \right)} - \pi
x4=πn−π+acos⁡(−1)x_{4} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}
x4=πnx_{4} = \pi n
Gráfica
0-80-60-40-2020406080-1001000200000
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
x1 = 0
x1=0x_{1} = 0 
x2 = pi
x2=πx_{2} = \pi 
x3 = 2*pi
x3=2πx_{3} = 2 \pi 
x3 = 2*pi
Suma y producto de raíces [src] 
suma
pi + 2*pi
π+2π\pi + 2 \pi 
=
3*pi
3π3 \pi 
producto
0*pi*2*pi
0π2π0 \pi 2 \pi 
=
0
00 
0
Respuesta numérica [src] 
x1 = 25.1327401464195
x2 = 6.28318528408307
x3 = -28.274333676669
x4 = 94.2477796093519
x5 = -21.9911485864129
x6 = -94.2477794213743
x7 = 97.389372828611
x8 = 0.0
x9 = 100.530964739312
x10 = 78.53981615825
x11 = -75.3982239115218
x12 = 3.14159153945546
x13 = 72.2566310277136
x14 = -34.5575187016351
x15 = 91.1061859604104
x16 = -3.14159313419367
x17 = 31.4159270619219
x18 = 40.8407040393519
x19 = 18.8495554527235
x20 = -72.2566308398808
x21 = -43.9822971744223
x22 = -50.265482258314
x23 = 62.8318526257023
x24 = 50.2654824463153
x25 = -78.5398158757739
x26 = -31.4159267482748
x27 = 12.5663704145927
x28 = 37.6991120687848
x29 = -87.9645943581507
x30 = -65.973445764663
x31 = 9.42477847373977
x32 = 59.6902602145004
x33 = -97.3893724932976
x34 = -84.8230005709274
x35 = -37.6991118775909
x36 = -6.28318509494079
x37 = -100.530964462409
x38 = -47.1238903089396
x39 = 28.2743338651162
x40 = 56.5486675771117
x41 = 43.9822971695754
x42 = -15.7079632968116
x43 = -12.5663701141083
x44 = -69.1150388967924
x45 = 87.9645943363399
x46 = 69.1150373568381
x47 = 75.3982242393431
x48 = -62.8318519640761
x49 = 59.690260650792
x50 = -56.5486672888531
x51 = -59.6902604582742
x52 = -91.1061874849821
x53 = 34.5575189958939
x54 = 84.8230012117849
x55 = 21.9911485852339
x56 = -25.1327417214108
x57 = 15.7079634868755
x58 = -81.6814090388783
x59 = -9.42477816679559
x60 = 65.9734457532278
x61 = -53.4070753298489
x62 = 53.4070756504516
x63 = 47.1238887521935
x64 = 81.681409232902
x64 = 81.681409232902
    © Sr Examen – Калькулятор