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- La ecuación:
-
Ecuación 3^x=7
- Ecuación x+y-4=0
-
Ecuación z^2+z+1=0
-
Ecuación 8*x=2
- Expresar {x} en función de y en la ecuación:
- -17*x-15*y=-17
- 12*x-20*y=10
- -20*x-13*y=15
- 9*x+14*y=-10
-
Expresiones idénticas
- sinh(iz)=-i
- seno hiperbólico de (iz) es igual a menos i
- sinhiz=-i
-
Expresiones semejantes
- sinh(iz)=+i
- sinh(i*z)=-2
-
Expresiones con funciones
- Seno hiperbólico sinh
- sinh(2*acosh(x/a))=0
- sinh(x)30
- sinh(i*z)=-2
- sinh(2*x)=1-x
- iz
- iz=1
- iz^2-(4+i)z+6+12i=0
sinh(iz)=-i la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\sinh{\left(i z \right)} = - i$$
es la ecuación trigonométrica más simple
La ecuación se convierte en
$$\sin{\left(z \right)} = -1$$
Esta ecuación se reorganiza en
$$z = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$z = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
O
$$z = 2 \pi n - \frac{\pi}{2}$$
$$z = 2 \pi n + \frac{3 \pi}{2}$$
, donde n es cualquier número entero
$$\sinh{\left(i z \right)} = - i$$
es la ecuación trigonométrica más simple
Dividamos ambos miembros de la ecuación en i
La ecuación se convierte en
$$\sin{\left(z \right)} = -1$$
Esta ecuación se reorganiza en
$$z = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$z = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
O
$$z = 2 \pi n - \frac{\pi}{2}$$
$$z = 2 \pi n + \frac{3 \pi}{2}$$
, donde n es cualquier número entero
Gráfica
Suma y producto de raíces
[src]
suma
pi 3*pi - -- + ---- 2 2
$$- \frac{\pi}{2} + \frac{3 \pi}{2}$$
=
pi
$$\pi$$
producto
-pi 3*pi ----*---- 2 2
$$- \frac{\pi}{2} \frac{3 \pi}{2}$$
=
2 -3*pi ------ 4
$$- \frac{3 \pi^{2}}{4}$$
-3*pi^2/4
Respuesta rápida
[src]
-pi
z1 = ----
2
$$z_{1} = - \frac{\pi}{2}$$
3*pi
z2 = ----
2
$$z_{2} = \frac{3 \pi}{2}$$
z2 = 3*pi/2
Respuesta numérica
[src]
z1 = -51.8362783335234
z2 = -83.2522042893833
z3 = 86.3937984838325
z4 = -95.8185763308148
z5 = -39.2699084145515
z6 = -102.101761026058
z7 = -20.4203527465087
z8 = -51.8362791922783
z9 = 48.6946866365921
z10 = 23.5619444059921
z11 = 54.9778710948428
z12 = 48.6946870830469
z13 = 67.5442408278864
z14 = -76.9690203748894
z15 = -1.57079581340397
z16 = -51.8362786893284
z17 = -32.9867224188086
z18 = 48.6946873020308
z19 = -45.5530929624673
z20 = -64.4026502975618
z21 = 73.8274274426229
z22 = -58.1194639976905
z23 = -14.1371674455661
z24 = 4.7123894841958
z25 = -7.85398119154045
z26 = 36.1283150875497
z27 = -89.5353906059052
z28 = 67.54424230971
z29 = 98.9601690454399
z30 = -20.420353265929
z31 = 10.9955739381756
z32 = 36.1283159497235
z33 = 42.4115013353669
z34 = 98.9601692809083
z35 = -1.57079643188553
z36 = -1.57079639503667
z37 = -89.535390750197
z38 = 61.2610563112167
z39 = 86.3937978309099
z40 = 80.1106122287081
z41 = -32.9867232184024
z42 = 538.783139388541
z43 = 54.9778718908148
z44 = 67.5442415586719
z45 = -45.5530935911043
z46 = 4.71238874329685
z47 = 73.8274274830848
z48 = -14.1371667858125
z49 = 80.1106131368654
z50 = -83.2522055723275
z51 = -70.6858331259916
z52 = -95.818575476176
z53 = -39.2699069219675
z54 = -95.8185758680502
z55 = -89.5353901118113
z56 = 80.1106130902139
z57 = 23.5619451518571
z58 = -64.4026498988255
z59 = 10.9955747360645
z60 = -70.6858351534454
z61 = 42.4115007162407
z62 = -39.2699076683741
z63 = 23.5619437708833
z64 = 48.6946859012172
z65 = 92.6769830592094
z66 = -76.9690195738024
z67 = -7.85398205280014
z68 = 92.6769837888103
z69 = -83.2522048211133
z70 = 92.6769843439965
z71 = 29.845130330036
z72 = 17.2787591562062
z73 = 29.8451303231501
z74 = -58.1194645939029
z75 = -26.7035379986821
z76 = -14.1371668370864
z77 = -45.5530935025548
z78 = 4.71239022926564
z79 = -7.85398149665124
z80 = -20.4203520060805
z81 = -70.6858343571487
z82 = 73.8274268520838
z83 = 42.4115007274741
z84 = -58.1194639046052
z85 = 61.2610571125526
z86 = -64.4026491641039
z87 = 17.2787599560783
z88 = 29.8451297031011
z89 = -26.7035372004893
z90 = 98.9601682515978
z91 = 86.3937978869933
z92 = 36.1283157235346
z92 = 36.1283157235346