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- La ecuación:
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Ecuación (x-3)*(x+2)=0
-
Ecuación (11x+14)-(5x-8)=25
-
Ecuación z^2-6*z+10=0
-
Ecuación 4/(x-4)=-5
- Expresar {x} en función de y en la ecuación:
- -7*x-13*y=5
- 15*x+1*y=19
- 7*x-1*y=-7
- -11*x-14*y=-3
-
Expresiones idénticas
- sin(tres *x)+cos(tres *x)= cero
- seno de (3 multiplicar por x) más coseno de (3 multiplicar por x) es igual a 0
- seno de (tres multiplicar por x) más coseno de (tres multiplicar por x) es igual a cero
- sin(3x)+cos(3x)=0
- sin3x+cos3x=0
- sin(3*x)+cos(3*x)=O
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Expresiones semejantes
- sqrt(3)sin3x+cos3x=1
- sin^3(x)+cos^3(x)=-1
- sin(3*x)-cos(3*x)=0
-
Expresiones con funciones
- Seno sin
- sin(x)=(-1)/sqrt(2)
- sin(x)=-5/2
- sin((pi*x)/4)=1
- sin(2*x)-sin(x)=0
- sin(5*x)-cos(4*x)=0
- Coseno cos
- cos(x)^2=cos(x)
- cos^2(x)=1
- cos(4*x)=0
- cos(pi*x)=-1
- cos(x)=x^2+1
sin(3*x)+cos(3*x)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
sin(3*x) + cos(3*x) = 0
$$\sin{\left(3 x \right)} + \cos{\left(3 x \right)} = 0$$
Solución detallada
Tenemos la ecuación
$$\sin{\left(3 x \right)} + \cos{\left(3 x \right)} = 0$$
cambiamos:
$$\frac{\sin{\left(3 x \right)}}{\cos{\left(3 x \right)}} = -1$$
o
$$\tan{\left(3 x \right)} = -1$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$3 x = \pi n + \operatorname{atan}{\left(1 \right)}$$
O
$$3 x = \pi n + \frac{\pi}{4}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$3$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{12}$$
$$\sin{\left(3 x \right)} + \cos{\left(3 x \right)} = 0$$
cambiamos:
$$\frac{\sin{\left(3 x \right)}}{\cos{\left(3 x \right)}} = -1$$
o
$$\tan{\left(3 x \right)} = -1$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$3 x = \pi n + \operatorname{atan}{\left(1 \right)}$$
O
$$3 x = \pi n + \frac{\pi}{4}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$3$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{12}$$
Suma y producto de raíces
[src]
suma
-pi ---- 12
$$- \frac{\pi}{12}$$
=
-pi ---- 12
$$- \frac{\pi}{12}$$
producto
-pi ---- 12
$$- \frac{\pi}{12}$$
=
-pi ---- 12
$$- \frac{\pi}{12}$$
-pi/12
Respuesta numérica
[src]
x1 = -23.3001455141243
x2 = -55.7632696012188
x3 = -46.3384916404494
x4 = -27.4889357189107
x5 = 78.2780169519457
x6 = 38.484510006475
x7 = 56.2868683768171
x8 = -73.565627971561
x9 = -71.4712328691678
x10 = 28.012534494509
x11 = -42.1497014356631
x12 = -66.2352451131848
x13 = 18.5877565337396
x14 = -35.8665161284835
x15 = -88.2263936883134
x16 = 91.8915851175014
x17 = 25.9181393921158
x18 = 58.3812634792103
x19 = -20.1585528605345
x20 = 76.1836218495525
x21 = -7.59218224617533
x22 = -44.2440965380563
x23 = -51.5744793964324
x24 = -49.4800842940392
x25 = -427.518400276011
x26 = 23.8237442897226
x27 = 82.4668071567321
x28 = -0.261799387799149
x29 = -13.8753675533549
x30 = 30.1069295969022
x31 = -93.4623814442964
x32 = 6.02138591938044
x33 = -99.7455667514759
x34 = -9.68657734856853
x35 = -31.6777259236971
x36 = -5.49778714378214
x37 = 16.4933614313464
x38 = 100.269165527074
x39 = -11.7809724509617
x40 = 12.30457122656
x41 = -81.9432083811338
x42 = 43.720497762458
x43 = -18.0641577581413
x44 = -95.5567765466895
x45 = 96.0803753222878
x46 = -62.0464549083984
x47 = 8.11578102177363
x48 = 67.8060414399797
x49 = -79.8488132787406
x50 = -97.6511716490827
x51 = -59.9520598060052
x52 = 60.4756585816035
x53 = 69.9004365423729
x54 = 52.0980781720307
x55 = -91.3679863419031
x56 = 47.9092879672443
x57 = 21.7293491873294
x58 = -37.9609112308767
x59 = -86.1319985859202
x60 = 54.1924732744239
x61 = 34.2957198016886
x62 = 89.7971900151083
x63 = -84.037603483527
x64 = 71.9948316447661
x65 = 14.3989663289532
x66 = 93.9859802198946
x67 = 36.3901149040818
x68 = 41.6261026600648
x69 = 50.0036830696375
x70 = -57.857664703612
x71 = -64.1408500107916
x72 = 3.92699081698724
x73 = 87.7027949127151
x74 = 32.2013246992954
x75 = -75.6600230739542
x76 = -53.6688744988256
x77 = 45.8148928648512
x78 = -77.7544181763474
x79 = 74.0892267471593
x80 = -69.3768377667746
x81 = 98.174770424681
x82 = 80.3724120543389
x83 = 1.83259571459405
x84 = -40.0553063332699
x85 = -15.9697626557481
x86 = 65.7116463375865
x87 = -29.5833308213039
x88 = 63.6172512351933
x89 = -22.2529479629277
x90 = -711.308936650289
x91 = -33.7721210260903
x92 = 10.2101761241668
x92 = 10.2101761241668
Gráfico