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- La ecuación:
-
Ecuación 8*x-3*(2*x+1)=2*x+4
-
Ecuación x^3=27
-
Ecuación 1+sin(x)=0
-
Ecuación 2*x^2+6*x+9=
- Expresar {x} en función de y en la ecuación:
- 20*x+6*y=8
- 7*x-19*y=-8
- -11*x+10*y=-9
- 6*x-2*y=20
- Gráfico de la función y =:
-
sin(3*x)
-
cos(2*x)
- Integral de d{x}:
- sin(3*x)
- cos(2*x)
- Derivada de:
-
sin(3*x)
-
cos(2*x)
-
Expresiones idénticas
- sin(tres *x)=cos(dos *x)
- seno de (3 multiplicar por x) es igual a coseno de (2 multiplicar por x)
- seno de (tres multiplicar por x) es igual a coseno de (dos multiplicar por x)
- sin(3x)=cos(2x)
- sin3x=cos2x
-
Expresiones semejantes
- sin^2(x)-2cos^2(x)-1/2=0
- arcsin3x
- sin5xcos3x-cos5xsin3x=-(sqrt(3)/2)
-
Expresiones con funciones
- Seno sin
- sin(x-pi/3)=0
- sin(x/2)=1/2
- sin^24𝑥−sin4𝑥−2=0
- sin(2*x)=-1/2
- sin(pi*x)=-1
- Coseno cos
- cos(pi*x)=1
- cos(x+(pi/6))=1
- cos(x)/3=0
- cos(2*x)+cos(x)=0
- cos(8*pi*x/6)=sqrt(3)/2
sin(3*x)=cos(2*x) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Respuesta rápida
[src]
pi
x1 = --
10
$$x_{1} = \frac{\pi}{10}$$
pi
x2 = --
2
$$x_{2} = \frac{\pi}{2}$$
/ ___________ ___________\
| ___ ___ / ___ ____ / ___ |
| I I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 |
x3 = -I*log|- - - ------- - -------------------- + ---------------------|
\ 4 4 8 8 /
$$x_{3} = - i \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)}$$
/ ___________ ___________ ___________ ___________\
| ___ / ___ ____ / ___ ____ / ___ ___ ___ / ___ |
| I \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 I*\/ 5 \/ 2 *\/ 5 - \/ 5 |
x4 = -I*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------|
\ 4 16 16 16 4 16 /
$$x_{4} = - i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} - \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}$$
/ ___________ ___________ ___________ ___________\
| ___ ___ / ___ ___ / ___ ____ / ___ ____ / ___ |
| I I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 2 *\/ 5 - \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 |
x5 = -I*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------|
\ 4 4 16 16 16 16 /
$$x_{5} = - i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)}$$
x5 = -i*log(-sqrt(10)*sqrt(sqrt(5) + 5)/16 - sqrt(2)*sqrt(sqrt(5) + 5)/16 - sqrt(2)*sqrt(5 - sqrt(5))/16 + sqrt(10)*sqrt(5 - sqrt(5))/16 - sqrt(5)*i/4 - i/4)
Suma y producto de raíces
[src]
suma
/ ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________ ___________ ___________\
| ___ ___ / ___ ____ / ___ | | ___ / ___ ____ / ___ ____ / ___ ___ ___ / ___ | | ___ ___ / ___ ___ / ___ ____ / ___ ____ / ___ |
pi pi | I I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 | | I \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 I*\/ 5 \/ 2 *\/ 5 - \/ 5 | | I I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 2 *\/ 5 - \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 |
-- + -- - I*log|- - - ------- - -------------------- + ---------------------| - I*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------| - I*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------|
10 2 \ 4 4 8 8 / \ 4 16 16 16 4 16 / \ 4 4 16 16 16 16 /
$$- i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} + \left(\left(- i \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} + \left(\frac{\pi}{10} + \frac{\pi}{2}\right)\right) - i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} - \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}\right)$$
=
/ ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________ ___________ ___________\
| ___ ___ / ___ ____ / ___ | | ___ ___ / ___ ___ / ___ ____ / ___ ____ / ___ | | ___ / ___ ____ / ___ ____ / ___ ___ ___ / ___ |
3*pi | I I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 | | I I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 2 *\/ 5 - \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 | | I \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 I*\/ 5 \/ 2 *\/ 5 - \/ 5 |
---- - I*log|- - - ------- - -------------------- + ---------------------| - I*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------| - I*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------|
5 \ 4 4 8 8 / \ 4 4 16 16 16 16 / \ 4 16 16 16 4 16 /
$$- i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} - i \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} + \frac{3 \pi}{5} - i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} - \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}$$
producto
/ / ___________ ___________\\ / / ___________ ___________ ___________ ___________\\ / / ___________ ___________ ___________ ___________\\
| | ___ ___ / ___ ____ / ___ || | | ___ / ___ ____ / ___ ____ / ___ ___ ___ / ___ || | | ___ ___ / ___ ___ / ___ ____ / ___ ____ / ___ ||
pi pi | | I I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 || | | I \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 I*\/ 5 \/ 2 *\/ 5 - \/ 5 || | | I I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 2 *\/ 5 - \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 ||
--*--*|-I*log|- - - ------- - -------------------- + ---------------------||*|-I*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------||*|-I*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------||
10 2 \ \ 4 4 8 8 // \ \ 4 16 16 16 4 16 // \ \ 4 4 16 16 16 16 //
$$- i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} - i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} - \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)} - i \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} \frac{\pi}{10} \frac{\pi}{2}$$
=
/ ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________ ___________ ___________\
| ___ ___ / ___ ____ / ___ | | ___ ___ / ___ ___ / ___ ____ / ___ ____ / ___ | | ___ / ___ ____ / ___ ____ / ___ ___ ___ / ___ |
2 | I I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 | | I I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 2 *\/ 5 - \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 | | I \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 I*\/ 5 \/ 2 *\/ 5 - \/ 5 |
I*pi *log|- - - ------- - -------------------- + ---------------------|*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------|*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------|
\ 4 4 8 8 / \ 4 4 16 16 16 16 / \ 4 16 16 16 4 16 /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
20
$$\frac{i \pi^{2} \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} - \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)} \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)}}{20}$$
i*pi^2*log(-i/4 - i*sqrt(5)/4 - sqrt(2)*sqrt(5 + sqrt(5))/8 + sqrt(10)*sqrt(5 + sqrt(5))/8)*log(-i/4 - i*sqrt(5)/4 - sqrt(2)*sqrt(5 + sqrt(5))/16 - sqrt(2)*sqrt(5 - sqrt(5))/16 - sqrt(10)*sqrt(5 + sqrt(5))/16 + sqrt(10)*sqrt(5 - sqrt(5))/16)*log(-i/4 - sqrt(2)*sqrt(5 + sqrt(5))/16 - sqrt(10)*sqrt(5 + sqrt(5))/16 - sqrt(10)*sqrt(5 - sqrt(5))/16 + i*sqrt(5)/4 + sqrt(2)*sqrt(5 - sqrt(5))/16)/20
Respuesta numérica
[src]
x1 = 26.7035374759771
x2 = 70.6858346085267
x3 = 61.8893752757189
x4 = -97.7035315266426
x5 = 88.2787535658732
x6 = -36.1283154253128
x7 = -37.3849525777185
x8 = 20.4203521560512
x9 = 58.1194641300388
x10 = 74.4557458900781
x11 = -42.41150070898
x12 = 98.3318500573605
x13 = 4.08407044966673
x14 = -23.5619448484475
x15 = 71.9424717672063
x16 = -83.8805238508475
x17 = 0.314159265358979
x18 = 83.2522057062651
x19 = 84.5088423815654
x20 = -67.5442421572865
x21 = 65.6592864600267
x22 = -98.960168969851
x23 = -5.96902604182061
x24 = 38.0132711084365
x25 = -33.6150413934108
x26 = -3082.21655243695
x27 = -76.340701482232
x28 = 85.7654794430014
x29 = 10.3672557568463
x30 = -93.9336203423348
x31 = -12.2522113490002
x32 = 7.85398173263687
x33 = 44.2964564156161
x34 = -56.2345084992573
x35 = 41.7831822927443
x36 = 34.2433599241287
x37 = -3.45575191894877
x38 = -73.8274272806455
x39 = -53.7212343763855
x40 = -19.7920337176157
x41 = -100.216805649514
x42 = 51.836278889862
x43 = 27.9601746169492
x44 = -61.2610567621223
x45 = 95.8185759411754
x46 = 24.1902634326414
x47 = 54.3495529071034
x48 = -66.2876049907446
x49 = -86.3937978510561
x50 = 20.4203523376058
x51 = 11.6238928182822
x52 = 30.473448739821
x53 = -26.0752190247953
x54 = 6.59734457253857
x55 = -77.5973385436679
x56 = 94.5619388730528
x57 = 14.1371670842217
x58 = 95.8185760463912
x59 = -29.8451300991422
x60 = -9.73893722612836
x61 = -87.6504350351552
x62 = -22.3053078404875
x63 = -17.2787596488556
x64 = 50.5796417227957
x65 = -43.6681378848981
x66 = 92.0486647501809
x67 = 81.9955682586936
x68 = 17.9070781254618
x69 = 97.0752129959246
x70 = -13.5088484104361
x71 = -63.7743308678728
x72 = 45.5530935642345
x73 = 340.862803294903
x74 = 68.1725605828985
x75 = -80.1106125840384
x76 = 1.57079642986981
x77 = -16.0221225333079
x78 = 64.4026493135056
x79 = -39.8982267005904
x80 = -49.9513231920777
x81 = -36.1283156488921
x82 = -57.4911455606932
x83 = -81.3672497279756
x84 = 21.6769893097696
x85 = -23.5619450008864
x86 = 48.0663675999238
x87 = -46.18141200777
x88 = 763.092855556961
x89 = -90.1637091580271
x90 = 78.2256570743859
x91 = -42.4115008665293
x92 = -60.0044196835651
x93 = -70.0575161750524
x94 = 89.5353906921091
x95 = -2.19911485751286
x95 = -2.19911485751286
Gráfico