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- La ecuación:
-
Ecuación x^2+5x=36
-
Ecuación 9-7(x+3)=5-6x
-
Ecuación 4x-5=3+2(x+1)
-
Ecuación 6/(x-2)+5/x=3
- Expresar {x} en función de y en la ecuación:
- -14*x-12*y=-13
- -20*x+14*y=16
- -7*x+15*y=-11
- -14*x+5*y=3
-
Expresiones idénticas
- sin(3t)+cos(3t)
- seno de (3t) más coseno de (3t)
- sin3t+cos3t
-
Expresiones semejantes
- sin(3t)-cos(3t)
-
Expresiones con funciones
- Seno sin
- sin(x)=1/2
- sin(x)-sqrt(2)/2=0
- sin(x)/x=1
- sin(x)=-0,5
- sin(x)=-1/7
- Coseno cos
- cos(2*x)+3*sin(x)+1=0
- cos(x)=4/7
- cos(x)/(sin(x)-1)=0
- cos^2(x)-1=0
- cos(x)=(2)/2
sin(3t)+cos(3t) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
sin(3*t) + cos(3*t) = 0
$$\sin{\left(3 t \right)} + \cos{\left(3 t \right)} = 0$$
Solución detallada
Tenemos la ecuación
$$\sin{\left(3 t \right)} + \cos{\left(3 t \right)} = 0$$
cambiamos:
$$\frac{\sin{\left(3 t \right)}}{\cos{\left(3 t \right)}} = -1$$
o
$$\tan{\left(3 t \right)} = -1$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$3 t = \pi n + \operatorname{atan}{\left(1 \right)}$$
O
$$3 t = \pi n + \frac{\pi}{4}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$3$$
obtenemos la respuesta:
$$t_{1} = \frac{\pi n}{3} + \frac{\pi}{12}$$
$$\sin{\left(3 t \right)} + \cos{\left(3 t \right)} = 0$$
cambiamos:
$$\frac{\sin{\left(3 t \right)}}{\cos{\left(3 t \right)}} = -1$$
o
$$\tan{\left(3 t \right)} = -1$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$3 t = \pi n + \operatorname{atan}{\left(1 \right)}$$
O
$$3 t = \pi n + \frac{\pi}{4}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$3$$
obtenemos la respuesta:
$$t_{1} = \frac{\pi n}{3} + \frac{\pi}{12}$$
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]
t1 = -95.5567765466895
t2 = 41.6261026600648
t3 = -84.037603483527
t4 = 80.3724120543389
t5 = 34.2957198016886
t6 = -55.7632696012188
t7 = -71.4712328691678
t8 = -22.2529479629277
t9 = 30.1069295969022
t10 = 93.9859802198946
t11 = 87.7027949127151
t12 = -29.5833308213039
t13 = -15.9697626557481
t14 = 82.4668071567321
t15 = -11.7809724509617
t16 = 60.4756585816035
t17 = 38.484510006475
t18 = -9.68657734856853
t19 = -91.3679863419031
t20 = 78.2780169519457
t21 = 76.1836218495525
t22 = -31.6777259236971
t23 = 23.8237442897226
t24 = 36.3901149040818
t25 = -77.7544181763474
t26 = -711.308936650289
t27 = 16.4933614313464
t28 = 69.9004365423729
t29 = 32.2013246992954
t30 = -51.5744793964324
t31 = -427.518400276011
t32 = -23.3001455141243
t33 = 14.3989663289532
t34 = 74.0892267471593
t35 = -75.6600230739542
t36 = 56.2868683768171
t37 = 63.6172512351933
t38 = -27.4889357189107
t39 = -62.0464549083984
t40 = -73.565627971561
t41 = -18.0641577581413
t42 = -7.59218224617533
t43 = 28.012534494509
t44 = -37.9609112308767
t45 = -97.6511716490827
t46 = 12.30457122656
t47 = -93.4623814442964
t48 = 47.9092879672443
t49 = -49.4800842940392
t50 = 67.8060414399797
t51 = -44.2440965380563
t52 = 54.1924732744239
t53 = -64.1408500107916
t54 = -86.1319985859202
t55 = -13.8753675533549
t56 = -0.261799387799149
t57 = -59.9520598060052
t58 = -66.2352451131848
t59 = -5.49778714378214
t60 = 21.7293491873294
t61 = -20.1585528605345
t62 = 3.92699081698724
t63 = -79.8488132787406
t64 = -69.3768377667746
t65 = -35.8665161284835
t66 = 10.2101761241668
t67 = 45.8148928648512
t68 = 100.269165527074
t69 = 8.11578102177363
t70 = -88.2263936883134
t71 = -33.7721210260903
t72 = 89.7971900151083
t73 = 43.720497762458
t74 = 71.9948316447661
t75 = -57.857664703612
t76 = -46.3384916404494
t77 = -53.6688744988256
t78 = 96.0803753222878
t79 = 25.9181393921158
t80 = 91.8915851175014
t81 = 52.0980781720307
t82 = -40.0553063332699
t83 = 98.174770424681
t84 = 18.5877565337396
t85 = 58.3812634792103
t86 = -81.9432083811338
t87 = 1.83259571459405
t88 = -42.1497014356631
t89 = 65.7116463375865
t90 = 50.0036830696375
t91 = 6.02138591938044
t92 = -99.7455667514759
t92 = -99.7455667514759