Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación x^2+6x+13=0
-
Ecuación (x+1)²+(x-6)²=2x²
- Ecuación 5x^2-125=0
-
Ecuación cos2x-1=0
- Expresar {x} en función de y en la ecuación:
- -20*x-18*y=-11
- -6*x-17*y=14
- 5*x-2*y=-14
- 15*x+14*y=19
-
Expresiones idénticas
- cos2x- uno = cero
- coseno de 2x menos 1 es igual a 0
- coseno de 2x menos uno es igual a cero
- cos2x-1=O
-
Expresiones semejantes
- (3tg^2)+(2cos^2x-1)=0
- 4cos^4(x)=11cos(2x)-1
- cos(2*x)-1=0
- cos2x+1=0
cos2x-1=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\cos{\left(2 x \right)} - 1 = 0$$
es la ecuación trigonométrica más simple
Obtenemos:
$$\cos{\left(2 x \right)} = 1$$
Esta ecuación se reorganiza en
$$2 x = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
O
$$2 x = \pi n$$
$$2 x = \pi n - \pi$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$2$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{2}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{2}$$
$$\cos{\left(2 x \right)} - 1 = 0$$
es la ecuación trigonométrica más simple
Transportemos -1 al miembro derecho de la ecuación
cambiando el signo de -1
Obtenemos:
$$\cos{\left(2 x \right)} = 1$$
Esta ecuación se reorganiza en
$$2 x = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
O
$$2 x = \pi n$$
$$2 x = \pi n - \pi$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$2$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{2}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{2}$$
Respuesta numérica
[src]
x1 = 81.6814091761104
x2 = -15.7079632965264
x3 = -47.1238900492539
x4 = -43.9822971745789
x5 = 9.42477821024198
x6 = -84.82300141007
x7 = 3.14159244884412
x8 = 47.123889589354
x9 = -21.9911485864515
x10 = -12.5663700417108
x11 = -91.1061872003049
x12 = 9.42477859080277
x13 = 40.8407042560881
x14 = -69.1150386737158
x15 = 15.7079634406648
x16 = -91.106187201329
x17 = -3.14159311568248
x18 = 69.1150385885879
x19 = 28.2743338652012
x20 = 34.5575190304759
x21 = -87.9645943587732
x22 = 25.1327410188866
x23 = 3.14159287686128
x24 = 97.3893725148693
x25 = -18.8495561207399
x26 = 18.8495554002244
x27 = 72.256631027719
x28 = 100.530964766599
x29 = -9.42477812668337
x30 = 53.4070753627408
x31 = 31.4159267865366
x32 = 84.8230010166547
x33 = 91.1061867314459
x34 = 56.5486676091327
x35 = -62.8318532583801
x36 = -25.132741632083
x37 = 84.8230014093114
x38 = -40.8407042660168
x39 = -31.4159267051849
x40 = 40.840703919946
x41 = -106.814150357553
x42 = 97.3893727097471
x43 = -37.6991118771514
x44 = 25.1327414478072
x45 = -12.5663703661411
x46 = 18.8495556796107
x47 = -53.4070752836338
x48 = 21.9911485851964
x49 = 75.3982239388525
x50 = 78.5398161878405
x51 = -72.2566308741333
x52 = 0.0
x53 = 31.4159271479423
x54 = -75.3982238620294
x55 = -84.8230018263493
x56 = 94.2477796093525
x57 = -81.6814090380061
x58 = -100.530964672522
x59 = -56.5486675191652
x60 = -59.6902604576401
x61 = -47.123890151099
x62 = 47.123890018392
x63 = -18.8495556944209
x64 = 69.1150381602162
x65 = -78.5398160958028
x66 = 6.28318528425126
x67 = -69.1150386253436
x68 = -25.132741473063
x69 = 62.8318524523063
x70 = -40.8407046898283
x71 = -94.2477794529919
x72 = -50.2654822953391
x73 = 59.6902605976901
x74 = 62.8318528326557
x75 = 91.1061871583643
x76 = -34.5575189426108
x77 = -6.28318513794069
x78 = 87.9645943357576
x79 = -1734.15914475848
x80 = 75.3982241944528
x81 = -3.14159289677385
x82 = -28.2743337166085
x83 = 53.4070756765307
x84 = 43.982297169427
x85 = -31.4159267959754
x86 = 65.9734457528975
x87 = -62.8318528379059
x88 = 37.6991120192083
x89 = 50.2654824463473
x90 = -34.5575189701076
x91 = -6371388.6625218
x92 = 12.5663704518704
x93 = -97.3893724403711
x94 = -65.9734457650176
x94 = -65.9734457650176
Gráfico