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- La ecuación:
-
Ecuación x=(x+1)/2
- Ecuación (x-6)(-5x-9)=0
-
Ecuación x^2-14*x+33=0
-
Ecuación 5-x^2=0
- Expresar {x} en función de y en la ecuación:
- -17*x-12*y=-9
- 18*x+17*y=-14
- 14*x-10*y=-4
- -17*x-8*y=7
- Derivada de:
-
sin(3x)
- Integral de d{x}:
- sin(3x)
- 1/7
- Forma canónica:
- sin(3x)
- Límite de la función:
- 1/7
-
Expresiones idénticas
- sin(3x)= uno / siete
- seno de (3x) es igual a 1 dividir por 7
- seno de (3x) es igual a uno dividir por siete
- sin3x=1/7
- sin(3x)=1 dividir por 7
-
Expresiones semejantes
- sin(3*x)-sin(2*x)=0
- sin3x=-(1)/(2)
- y-sin3x*y=x^3*e^((-1/3)cos3x)
- 2*sin(3*x)=0
- 2*(1+sin(3*x)),x=0
-
Expresiones con funciones
- Seno sin
- sin(x)-2*x-1=0
- sin(1)/((3*x))=-1
- sin(pi*(x^2+1)/(x^2+11))=1/2
- sin(x)-2sqrt(x)=0
- sin(4*a)+cos(2*a)+sin(2*a)*cos(2*a)=1
sin(3x)=1/7 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\sin{\left(3 x \right)} = \frac{1}{7}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$3 x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{7} \right)}$$
$$3 x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{7} \right)} + \pi$$
O
$$3 x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{7} \right)}$$
$$3 x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{7} \right)} + \pi$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$3$$
obtenemos la respuesta:
$$x_{1} = \frac{2 \pi n}{3} + \frac{\operatorname{asin}{\left(\frac{1}{7} \right)}}{3}$$
$$x_{2} = \frac{2 \pi n}{3} - \frac{\operatorname{asin}{\left(\frac{1}{7} \right)}}{3} + \frac{\pi}{3}$$
$$\sin{\left(3 x \right)} = \frac{1}{7}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$3 x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{7} \right)}$$
$$3 x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{7} \right)} + \pi$$
O
$$3 x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{7} \right)}$$
$$3 x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{7} \right)} + \pi$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$3$$
obtenemos la respuesta:
$$x_{1} = \frac{2 \pi n}{3} + \frac{\operatorname{asin}{\left(\frac{1}{7} \right)}}{3}$$
$$x_{2} = \frac{2 \pi n}{3} - \frac{\operatorname{asin}{\left(\frac{1}{7} \right)}}{3} + \frac{\pi}{3}$$
Respuesta rápida
[src]
asin(1/7) pi
x1 = - --------- + --
3 3
$$x_{1} = - \frac{\operatorname{asin}{\left(\frac{1}{7} \right)}}{3} + \frac{\pi}{3}$$
asin(1/7)
x2 = ---------
3
$$x_{2} = \frac{\operatorname{asin}{\left(\frac{1}{7} \right)}}{3}$$
x2 = asin(1/7)/3
Suma y producto de raíces
[src]
suma
asin(1/7) pi asin(1/7)
- --------- + -- + ---------
3 3 3
$$\frac{\operatorname{asin}{\left(\frac{1}{7} \right)}}{3} + \left(- \frac{\operatorname{asin}{\left(\frac{1}{7} \right)}}{3} + \frac{\pi}{3}\right)$$
=
pi -- 3
$$\frac{\pi}{3}$$
producto
/ asin(1/7) pi\ asin(1/7) |- --------- + --|*--------- \ 3 3 / 3
$$\left(- \frac{\operatorname{asin}{\left(\frac{1}{7} \right)}}{3} + \frac{\pi}{3}\right) \frac{\operatorname{asin}{\left(\frac{1}{7} \right)}}{3}$$
=
(pi - asin(1/7))*asin(1/7)
--------------------------
9
$$\frac{\left(\pi - \operatorname{asin}{\left(\frac{1}{7} \right)}\right) \operatorname{asin}{\left(\frac{1}{7} \right)}}{9}$$
(pi - asin(1/7))*asin(1/7)/9
Respuesta numérica
[src]
x1 = 8.42536293254124
x2 = 48.218869878012
x3 = 44.0300796732256
x4 = 85.9179817210895
x5 = -48.123304832075
x6 = -50.2176999344682
x7 = 41.9356845708324
x8 = -39.7457244225023
x9 = -19.9445359957038
x10 = 17.7545758473737
x11 = -87.9168117775458
x12 = -76.4932037603201
x13 = -52.3120950368614
x14 = -70.2100184531405
x15 = -24.1333262004902
x16 = 2.14217762536165
x17 = -63.9268331459609
x18 = 88.0123768234827
x19 = -46.0289097296818
x20 = 90.1067719258759
x21 = -55.5492527363881
x22 = -72.3044135555337
x23 = -77.4448362655798
x24 = 68.0200583048104
x25 = -61.8324380435677
x26 = -59.7380429411745
x27 = 26.1321562569465
x28 = 4.23657272775485
x29 = 96.3899572330555
x30 = -22.038931098097
x31 = 34.5097366665193
x32 = 98.4843523354486
x33 = 76.3976387143832
x34 = -99.5315498866452
x35 = 15.6601807449805
x36 = 58.6908453899779
x37 = -9.47256048373784
x38 = 70.1144534072036
x39 = -92.1056019823321
x40 = 0.0477825229684551
x41 = -68.1156233507473
x42 = 100.578747437842
x43 = 94.2955621306622
x44 = -13.6613506885242
x45 = -43.9345146272886
x46 = 72.2088485095968
x47 = -81.6336264703662
x48 = 13.5657856425873
x49 = -796.965118983579
x50 = -28.3221164052766
x51 = -73.2560460607934
x52 = 63.831268100024
x53 = -66.0212282483541
x54 = 46.1244747756188
x55 = 71.2572160043371
x56 = -85.8224166751526
x57 = 54.5020551851915
x58 = -41.8401195248955
x59 = -79.539231367973
x60 = 24.0377611545533
x61 = -4.14100768181794
x62 = -17.8501408933106
x63 = -2.04661257942474
x64 = 19.8489709497669
x65 = 92.2011670282691
x66 = -57.6436478387813
x67 = 81.7291915163031
x68 = 39.8412894684392
x69 = 6.33096783014804
x70 = 52.4076600827983
x71 = 21.9433660521601
x72 = 50.3132649804051
x73 = -90.011206879939
x74 = -97.437154784252
x75 = 10.5197580349344
x76 = 37.746894366046
x77 = -33.4625391153227
x78 = 65.9256632024172
x79 = 32.4153415641261
x80 = 28.2265513593397
x81 = 83.8235866186963
x82 = -11.566955586131
x83 = 74.30324361199
x84 = -37.6513293201091
x85 = 78.4920338167764
x86 = -83.7280215727594
x87 = -94.1999970847253
x88 = -26.2277213028834
x89 = -35.5569342177159
x90 = -246.139207054169
x91 = -15.7557457909174
x92 = 61.7368729976308
x93 = -6.23540278421113
x94 = 30.3209464617329
x94 = 30.3209464617329