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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
- 10*x+3*y=2
- 14*x-10*y=-4
- Derivada de:
-
2sin(3x)
-
-1/2
- Integral de d{x}:
- -1/2
- Suma de la serie:
-
-1/2
-
Expresiones idénticas
- dos sin(3x)=- uno /2
- 2 seno de (3x) es igual a menos 1 dividir por 2
- dos seno de (3x) es igual a menos uno dividir por 2
- 2sin3x=-1/2
- 2sin(3x)=-1 dividir por 2
-
Expresiones semejantes
- sin(4x)+sin(2*x)+2sin(3*x)=0
- 2*sin(3*x)=0
- 2sin(3x-3)+1=0
- 2*sin(3*x)^cos(3*x)=-1/2
- 2sin(3x)=+1/2
2sin(3x)=-1/2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$2 \sin{\left(3 x \right)} = - \frac{1}{2}$$
es la ecuación trigonométrica más simple
La ecuación se convierte en
$$\sin{\left(3 x \right)} = - \frac{1}{4}$$
Esta ecuación se reorganiza en
$$3 x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{4} \right)}$$
$$3 x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{4} \right)} + \pi$$
O
$$3 x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{4} \right)}$$
$$3 x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{4} \right)} + \pi$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$3$$
obtenemos la respuesta:
$$x_{1} = \frac{2 \pi n}{3} - \frac{\operatorname{asin}{\left(\frac{1}{4} \right)}}{3}$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{\operatorname{asin}{\left(\frac{1}{4} \right)}}{3} + \frac{\pi}{3}$$
$$2 \sin{\left(3 x \right)} = - \frac{1}{2}$$
es la ecuación trigonométrica más simple
Dividamos ambos miembros de la ecuación en 2
La ecuación se convierte en
$$\sin{\left(3 x \right)} = - \frac{1}{4}$$
Esta ecuación se reorganiza en
$$3 x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{4} \right)}$$
$$3 x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{4} \right)} + \pi$$
O
$$3 x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{4} \right)}$$
$$3 x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{4} \right)} + \pi$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$3$$
obtenemos la respuesta:
$$x_{1} = \frac{2 \pi n}{3} - \frac{\operatorname{asin}{\left(\frac{1}{4} \right)}}{3}$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{\operatorname{asin}{\left(\frac{1}{4} \right)}}{3} + \frac{\pi}{3}$$
Suma y producto de raíces
[src]
suma
pi asin(1/4) asin(1/4) -- + --------- - --------- 3 3 3
$$- \frac{\operatorname{asin}{\left(\frac{1}{4} \right)}}{3} + \left(\frac{\operatorname{asin}{\left(\frac{1}{4} \right)}}{3} + \frac{\pi}{3}\right)$$
=
pi -- 3
$$\frac{\pi}{3}$$
producto
/pi asin(1/4)\ -asin(1/4) |-- + ---------|*----------- \3 3 / 3
$$\left(\frac{\operatorname{asin}{\left(\frac{1}{4} \right)}}{3} + \frac{\pi}{3}\right) \left(- \frac{\operatorname{asin}{\left(\frac{1}{4} \right)}}{3}\right)$$
=
-(pi + asin(1/4))*asin(1/4)
----------------------------
9
$$- \frac{\left(\operatorname{asin}{\left(\frac{1}{4} \right)} + \pi\right) \operatorname{asin}{\left(\frac{1}{4} \right)}}{9}$$
-(pi + asin(1/4))*asin(1/4)/9
Respuesta rápida
[src]
pi asin(1/4)
x1 = -- + ---------
3 3
$$x_{1} = \frac{\operatorname{asin}{\left(\frac{1}{4} \right)}}{3} + \frac{\pi}{3}$$
-asin(1/4)
x2 = -----------
3
$$x_{2} = - \frac{\operatorname{asin}{\left(\frac{1}{4} \right)}}{3}$$
x2 = -asin(1/4)/3
Respuesta numérica
[src]
x1 = 36.7361410435949
x2 = -85.954425949835
x3 = 63.9632773747065
x4 = -2.17862185410722
x5 = -13.5293414138417
x6 = -17.7181316186281
x7 = -88.0488210522282
x8 = 89.9747626511934
x9 = -81.7656357450487
x10 = -35.6889434923984
x11 = 80.7184381938521
x12 = 56.4644410129022
x13 = -31.500153287612
x14 = 92.0691577535866
x15 = 10.387748760252
x16 = -50.3497092091507
x17 = -19.8125267210213
x18 = -282.827565574795
x19 = -4.27301695650042
x20 = -70.078009178458
x21 = 22.0753753268426
x22 = -90.1432161546214
x23 = -94.3320063594078
x24 = -67.9836140760648
x25 = 66.0576724770997
x26 = -92.2376112570146
x27 = 26.264165531629
x28 = -59.606033666492
x29 = -32.3788973353805
x30 = -95.2107504071764
x31 = -72.1724042808512
x32 = 28.3585606340222
x33 = -44.9452679497397
x34 = 45.9924655009363
x35 = 59.7744871699201
x36 = -41.9721287995779
x37 = 72.3408577842793
x38 = -28.1901071305941
x39 = -74.2667993832444
x40 = 39.7092801937567
x41 = -65.8892189736716
x42 = 61.8688822723133
x43 = 48.0868606033295
x44 = 87.0016235010316
x45 = -0.0842267517140262
x46 = 15.792190019663
x47 = 96.257947958373
x48 = -46.1609190043643
x49 = 52.2756508081159
x50 = -57.5116385640989
x51 = 79.5027871392274
x52 = 30.4529557364154
x53 = -79.6712406426554
x54 = 54.3700459105091
x55 = 17.8865851220562
x56 = -75.4824504378691
x57 = 2.01016835067917
x58 = -39.8777336971847
x59 = -83.8600308474418
x60 = -33.5945483900052
x61 = 8.29335365785876
x62 = 94.1635528559798
x63 = -55.4172434617057
x64 = -77.5768455402623
x65 = 32.5473508388086
x66 = 41.8036752961499
x67 = -37.7833385947915
x68 = -11.4349463114485
x69 = -21.9069218234145
x70 = 24.1697704292358
x71 = -44.0665239019711
x72 = -63.7948238712784
x73 = -48.2553141067575
x74 = 4.10456345307237
x75 = -920.402420750095
x76 = 83.6915773440138
x77 = 19.9809802244494
x78 = -26.0957120282009
x79 = 50.1812557057227
x80 = 87.8803675488002
x81 = 100.446738163159
x82 = 43.8980703985431
x83 = 76.5296479890657
x84 = 35.5204899889703
x85 = 58.5588361152954
x86 = 85.785972446407
x87 = 6.19895855546556
x88 = -61.7004287688852
x89 = -99.3995406119628
x90 = 12.4821438626451
x91 = -15.6237365162349
x92 = -24.0013169258077
x93 = 98.3523430607662
x94 = 70.2464626818861
x95 = 68.1520675794929
x96 = 74.4352528866725
x96 = 74.4352528866725