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- La ecuación:
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Ecuación 3^x=2
-
Ecuación (x-11)*(-x+9)=0
-
Ecuación 8*x=2
-
Ecuación 3^x=81
- Expresar {x} en función de y en la ecuación:
- 4*x-1*y=-3
- -11*x+9*y=-20
- 9*x+17*y=13
- -5*x+6*y=-8
-
Expresiones idénticas
- tg(5x)=sqrt dos /2
- tg(5x) es igual a raíz cuadrada de 2 dividir por 2
- tg(5x) es igual a raíz cuadrada de dos dividir por 2
- tg(5x)=√2/2
- tg5x=sqrt2/2
- tg(5x)=sqrt2 dividir por 2
-
Expresiones semejantes
- cos(2*pi/(sqrt(x)))=sqrt(2)/2
- cos(2*pi*x)/(4)=sqrt(2)/2
- U=tg(5*x)/y^3-2sin^1/2*(z)
- sin(x-pi/4)+sqrt(2)/2=0
- cos(6x)=sqrt(2)/2
-
Expresiones con funciones
- tg
- tgπ(4x−5)6=3–√3
- tg2πx9+4sin2πx9−6=0,
- tg(x)=7/2
- tg2x-ctg3x=0
- tgt=-1
tg(5x)=sqrt2/2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\tan{\left(5 x \right)} = \frac{\sqrt{2}}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$5 x = \pi n + \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}$$
O
$$5 x = \pi n + \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$5$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{5} + \frac{\operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{5}$$
$$\tan{\left(5 x \right)} = \frac{\sqrt{2}}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$5 x = \pi n + \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}$$
O
$$5 x = \pi n + \operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$5$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{5} + \frac{\operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{5}$$
Suma y producto de raíces
[src]
suma
/ ___\
|\/ 2 |
atan|-----|
\ 2 /
-----------
5
$$\frac{\operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{5}$$
=
/ ___\
|\/ 2 |
atan|-----|
\ 2 /
-----------
5
$$\frac{\operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{5}$$
producto
/ ___\
|\/ 2 |
atan|-----|
\ 2 /
-----------
5
$$\frac{\operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{5}$$
=
/ ___\
|\/ 2 |
atan|-----|
\ 2 /
-----------
5
$$\frac{\operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{5}$$
atan(sqrt(2)/2)/5
Respuesta rápida
[src]
/ ___\
|\/ 2 |
atan|-----|
\ 2 /
x1 = -----------
5
$$x_{1} = \frac{\operatorname{atan}{\left(\frac{\sqrt{2}}{2} \right)}}{5}$$
x1 = atan(sqrt(2)/2)/5
Respuesta numérica
[src]
x1 = -13.699911734061
x2 = 89.9726458344022
x3 = 0.123095941734077
x4 = -81.5583130516005
x5 = -33.8061047170357
x6 = -79.6733574594467
x7 = -23.7530082255484
x8 = 34.0522966005038
x9 = 12.0611480253753
x10 = -5.53177083472755
x11 = 28.3974298240422
x12 = 38.4505263155296
x13 = 26.5124742318883
x14 = -83.4432686437544
x15 = 40.3354819076834
x16 = 80.5478678736328
x17 = -45.7441568006769
x18 = 62.326630482812
x19 = -52.0273421078565
x20 = 10.1761924332214
x21 = 13.9461036175292
x22 = 92.485919957274
x23 = 84.3177790579405
x24 = -77.7884018672928
x25 = -85.9565427666263
x26 = 4.52132565675979
x27 = -15.5848673262149
x28 = -3.64681524257367
x29 = -61.4521200686259
x30 = -41.9742456163692
x31 = 76.1496381586071
x32 = 70.4947713821454
x33 = 96.2558311415818
x34 = -57.6822088843181
x35 = 72.3797269742993
x36 = -93.4963651352418
x37 = -1.7618596504198
x38 = -31.9211491248818
x39 = -39.4609714934973
x40 = 74.2646825664532
x41 = -19.9830970412406
x42 = 60.4416748906581
x43 = 64.2115860749659
x44 = -75.9034462751389
x45 = -63.9653941914977
x46 = 86.2027346500944
x47 = 20.2292889247088
x48 = 48.5036228070169
x49 = -99.7795504424214
x50 = -17.4698229183688
x51 = 23.9992001090165
x52 = 35.9372521926577
x53 = -53.9122977000104
x54 = 58.5567192985042
x55 = -9.93000054975326
x56 = 8.29123684106754
x57 = 18.3443333325549
x58 = 78.0345937507609
x59 = -65.8503497836516
x60 = 94.3708755494279
x61 = -25.6379638177022
x62 = 6.40628124891366
x63 = -8.04504495759939
x64 = 100.025742325889
x65 = 50.3885783991708
x66 = -30.0361935327279
x67 = -47.6291123928308
x68 = 2.00805153388795
x69 = -43.859201208523
x70 = 98.1407867337356
x71 = -49.5140679849847
x72 = 32.16734100835
x73 = 22.1142445168626
x74 = 66.0965416671197
x75 = -11.8149561419071
x76 = -69.6202609679593
x77 = 52.2735339913246
x78 = -37.5760159013434
x79 = 42.2204374998373
x80 = -59.567164476472
x81 = 44.1053930919912
x82 = 30.2823854161961
x83 = 54.1584895834785
x84 = -27.5229194098561
x85 = -87.8414983587801
x86 = 67.9814972592736
x87 = -74.018490682985
x88 = 56.0434451756324
x89 = -89.726453950934
x90 = -35.6910603091896
x91 = -91.6114095430879
x92 = -97.8945948502675
x93 = -21.8680526333945
x94 = 45.9903486841451
x95 = -67.7353053758055
x96 = 88.0876902422483
x97 = -71.5052165601132
x98 = 16.459377740401
x99 = 82.4328234657867
x100 = -55.7972532921642
x101 = -96.0096392581136
x101 = -96.0096392581136