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- La ecuación:
-
Ecuación x^3-x^2-x-1=0
-
Ecuación 12-4(x-3)=39-9x
-
Ecuación 0,2x+2,7=1,4-1,1x
-
Ecuación x^2=2x+8
- Expresar {x} en función de y en la ecuación:
- -11*x-14*y=-3
- -9*x-1*y=6
- -2*x+2*y=4
- -11*x-3*y=14
- Gráfico de la función y =:
-
sin(2*x)
- sin((x+pi)/2)
- Integral de d{x}:
- sin(2*x)
- Derivada de:
-
sin(2*x)
-
Expresiones idénticas
- sin(dos *x)=sin((x+pi)/ dos)
- seno de (2 multiplicar por x) es igual a seno de ((x más número pi ) dividir por 2)
- seno de (dos multiplicar por x) es igual a seno de ((x más número pi ) dividir por dos)
- sin(2x)=sin((x+pi)/2)
- sin2x=sinx+pi/2
- sin(2*x)=sin((x+pi) dividir por 2)
-
Expresiones semejantes
- sin(2*x)=sin((x-pi)/2)
- sin2xcosx-sinxcos2x=1
- sin(2x)=-1/2
- sin(2*x)=sqrt(2)*sin(x+pi/2)
- sin(x+pi/2)=0
- cos(2*x)=sin(x+pi/2)
- sin^2(x)-2sqrt3*sin(x)*cos(x)-3*cos^2(x)=0
- 4*sin(2x)+4*cos(4x)=1
-
Expresiones con funciones
- Seno sin
- sin(x)=1/3
- sin(6*x)=9/8
- sin(2x)=-1/2
- sin(3*x)-cos(3*x)=0
- sin(x)^(2)-sin(x)=0
- Seno sin
- sin(x)=1/3
- sin(6*x)=9/8
- sin(2x)=-1/2
- sin(3*x)-cos(3*x)=0
- sin(x)^(2)-sin(x)=0
sin(2*x)=sin((x+pi)/2) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/x + pi\
sin(2*x) = sin|------|
\ 2 /
$$\sin{\left(2 x \right)} = \sin{\left(\frac{x + \pi}{2} \right)}$$
Respuesta rápida
[src]
pi
x1 = --
5
$$x_{1} = \frac{\pi}{5}$$
pi
x2 = --
3
$$x_{2} = \frac{\pi}{3}$$
x3 = pi
$$x_{3} = \pi$$
/ ___________ ___________\
| ___ ___ / ___ ____ / ___ |
| I I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 |
x4 = -2*I*log|- - - ------- - -------------------- + ---------------------|
\ 4 4 8 8 /
$$x_{4} = - 2 i \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)}$$
/ ___________ ___________ ___________ ___________\
| ___ / ___ ____ / ___ ____ / ___ ___ ___ / ___ |
| I \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 I*\/ 5 \/ 2 *\/ 5 - \/ 5 |
x5 = -2*I*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------|
\ 4 16 16 16 4 16 /
$$x_{5} = - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} - \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}$$
/ ___________ ___________ ___________ ___________\
| ___ ___ / ___ ___ / ___ ____ / ___ ____ / ___ |
| I I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 2 *\/ 5 - \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 |
x6 = -2*I*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------|
\ 4 4 16 16 16 16 /
$$x_{6} = - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)}$$
x6 = -2*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 |
-- + -- + pi - 2*I*log|- - - ------- - -------------------- + ---------------------| - 2*I*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------| - 2*I*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------|
5 3 \ 4 4 8 8 / \ 4 16 16 16 4 16 / \ 4 4 16 16 16 16 /
$$- 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} + \left(\left(- 2 i \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} + \left(\left(\frac{\pi}{5} + \frac{\pi}{3}\right) + \pi\right)\right) - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} - \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}\right)$$
=
/ ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________ ___________ ___________\
| ___ ___ / ___ ____ / ___ | | ___ ___ / ___ ___ / ___ ____ / ___ ____ / ___ | | ___ / ___ ____ / ___ ____ / ___ ___ ___ / ___ |
23*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 |
----- - 2*I*log|- - - ------- - -------------------- + ---------------------| - 2*I*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------| - 2*I*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------|
15 \ 4 4 8 8 / \ 4 4 16 16 16 16 / \ 4 16 16 16 4 16 /
$$- 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} + \frac{23 \pi}{15} - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} - \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}$$
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 |
--*--*pi*-2*I*log|- - - ------- - -------------------- + ---------------------|*-2*I*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------|*-2*I*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------|
5 3 \ 4 4 8 8 / \ 4 16 16 16 4 16 / \ 4 4 16 16 16 16 /
$$- 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} - \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} \pi \frac{\pi}{5} \frac{\pi}{3}$$
=
/ ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________ ___________ ___________\
| ___ ___ / ___ ____ / ___ | | ___ ___ / ___ ___ / ___ ____ / ___ ____ / ___ | | ___ / ___ ____ / ___ ____ / ___ ___ ___ / ___ |
3 | 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 |
8*I*pi *log|- - - ------- - -------------------- + ---------------------|*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------|*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------|
\ 4 4 8 8 / \ 4 4 16 16 16 16 / \ 4 16 16 16 4 16 /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
15
$$\frac{8 i \pi^{3} \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} - \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)} \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)}}{15}$$
8*i*pi^3*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)/15
Respuesta numérica
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x1 = -92.3628240155399
x2 = 88.5929128312322
x3 = 34.5575191894877
x4 = -89.8495498926681
x5 = -243.15927138785
x6 = 805.294916870184
x7 = 96.1327351998477
x8 = -87.3362757697962
x9 = -34.5575191894877
x10 = -414.061911743135
x11 = 28.2743338823081
x12 = -79.7964534011807
x13 = 43.3539786195391
x14 = 42.9350995990605
x15 = 59.6902604182061
x16 = -49.6371639267187
x17 = 93.6194610769758
x18 = -64.7168086639497
x19 = 63.8790506229925
x20 = 15.707963267949
x21 = 13.6135681655558
x22 = -15.707963267949
x23 = 35.8141562509236
x24 = -72.2566310325652
x25 = 30.3687289847013
x26 = 40.8407044966673
x27 = 53.4070751110265
x28 = 45.867252742411
x29 = -42.0973415581032
x30 = 65.9734457253857
x31 = -14.451326206513
x32 = -52.1504380495906
x33 = -19.8967534727354
x34 = 21.9911485751286
x35 = -65.9734457253857
x36 = -74.3510261349584
x37 = 78.5398163397448
x38 = -195.407063053285
x39 = -37.0707933123596
x40 = 101.57816246607
x41 = 76.026542216873
x42 = -36.6519142918809
x43 = 70.9999939711293
x44 = -82.3097275240526
x45 = 73.5132680940012
x46 = -24.0855436775217
x47 = -97.3893722612836
x48 = 26.1799387799149
x49 = -39.5840674352314
x50 = -21.9911485751286
x51 = 58.4336233567702
x52 = -69.7433569096934
x53 = -53.4070751110265
x54 = 55.9203492338983
x55 = 18.2212373908208
x56 = 23.2477856365645
x57 = -45.0294947014537
x58 = -59.6902604182061
x59 = -57.5958653158129
x60 = 20.7345115136926
x61 = 86.0796387083603
x62 = -1.88495559215388
x63 = -11.9380520836412
x64 = 51.3126800086333
x65 = -28.2743338823081
x66 = -29.5309709437441
x67 = -94.8760981384118
x68 = 101.159283445591
x69 = -61.7846555205993
x70 = -7.33038285837618
x71 = 0.628318530717959
x72 = -95.2949771588904
x73 = 50.8938009881547
x74 = -67.2300827868216
x75 = -9.42477796076938
x76 = 80.634211442138
x77 = 38.3274303737955
x78 = 72.2566310325652
x79 = -44.6106156809751
x80 = 5.65486677646163
x81 = 3695.14127915231
x82 = 48.3805268652828
x83 = -32.0442450666159
x84 = 9.42477796076938
x85 = 68.0678408277789
x86 = -78.5398163397448
x87 = 8.16814089933346
x88 = -99.9026463841554
x88 = -99.9026463841554