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- La ecuación:
-
Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
-
Ecuación x^2+4=5x
-
Ecuación x(x^2+2x+1)=6(x+1)
-
Ecuación 4x+1=-3x+15
- Expresar {x} en función de y en la ecuación:
- -6*x-20*y=8
- 13*x-12*y=19
- -9*x+11*y=9
- -4*x-8*y=-20
- Derivada de:
-
sin(6x)
-
cos(2x)
- Integral de d{x}:
- sin(6x)
- cos(2x)
- Gráfico de la función y =:
-
cos(2x)
-
Expresiones idénticas
- sin(6x)=cos(2x)
- seno de (6x) es igual a coseno de (2x)
- sin6x=cos2x
-
Expresiones semejantes
- -3sinx-1+cos^2(x)=0
- sin2x+sin6x=соs2x
- sin(6x+пи)=-√2/2
- 3*sin(x)^(2)-3*x-(5/2)*sin(6*x)+1=0
- cos^2(x)=(1/2)
- cos(2*x)+cos(8*x)-cos(6*x)=1
- cos^2x=1
-
Expresiones con funciones
- Seno sin
- sin(x)=pi
- sin(4*x)=0
- sin(x)^2=1
- sin(x)=(1/2)
- sin(x)=0,5
- Coseno cos
- cos(x)=-(4/5)
- cos(x+(pi/6))=-1
- cos(3*x)=1
- cos(x)=-3/2
- cos(x)=1/2
sin(6x)=cos(2x) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Respuesta rápida
[src]
-7*pi
x1 = -----
8
$$x_{1} = - \frac{7 \pi}{8}$$
-3*pi
x2 = -----
8
$$x_{2} = - \frac{3 \pi}{8}$$
pi
x3 = --
16
$$x_{3} = \frac{\pi}{16}$$
pi
x4 = --
8
$$x_{4} = \frac{\pi}{8}$$
5*pi
x5 = ----
8
$$x_{5} = \frac{5 \pi}{8}$$
/ 16____\ x6 = -I*log\-\/ -1 /
$$x_{6} = - i \log{\left(- \sqrt[16]{-1} \right)}$$
/ /pi\\
|cos|--|| / _____________________\
| \16/| | / 2/pi\ 2/pi\ |
x7 = pi - atan|-------| - I*log| / cos |--| + sin |--| |
| /pi\| \\/ \16/ \16/ /
|sin|--||
\ \16//
$$x_{7} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{16} \right)}}{\sin{\left(\frac{\pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{16} \right)} + \cos^{2}{\left(\frac{\pi}{16} \right)}} \right)} + \pi$$
/ /pi\\
|cos|--|| / _____________________\
| \16/| | / 2/pi\ 2/pi\ |
x8 = - atan|-------| - I*log| / cos |--| + sin |--| |
| /pi\| \\/ \16/ \16/ /
|sin|--||
\ \16//
$$x_{8} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{16} \right)}}{\sin{\left(\frac{\pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{16} \right)} + \cos^{2}{\left(\frac{\pi}{16} \right)}} \right)}$$
/ /3*pi\\
/ _________________________\ |cos|----||
| / 2/3*pi\ 2/3*pi\ | | \ 16 /|
x9 = -pi - I*log| / cos |----| + sin |----| | + atan|---------|
\\/ \ 16 / \ 16 / / | /3*pi\|
|sin|----||
\ \ 16 //
$$x_{9} = - \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \cos^{2}{\left(\frac{3 \pi}{16} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{3 \pi}{16} \right)}} \right)}$$
/ /5*pi\\
/ _________________________\ |sin|----||
| / 2/3*pi\ 2/5*pi\ | | \ 16 /|
x10 = - I*log| / sin |----| + sin |----| | + atan|---------|
\\/ \ 16 / \ 16 / / | /3*pi\|
|sin|----||
\ \ 16 //
$$x_{10} = - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \sin^{2}{\left(\frac{5 \pi}{16} \right)}} \right)} + \operatorname{atan}{\left(\frac{\sin{\left(\frac{5 \pi}{16} \right)}}{\sin{\left(\frac{3 \pi}{16} \right)}} \right)}$$
/ /3*pi\\
|sin|----|| / _________________________\
| \ 16 /| | / 2/3*pi\ 2/5*pi\ |
x11 = pi - atan|---------| - I*log| / sin |----| + sin |----| |
| /5*pi\| \\/ \ 16 / \ 16 / /
|sin|----||
\ \ 16 //
$$x_{11} = - \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{5 \pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \sin^{2}{\left(\frac{5 \pi}{16} \right)}} \right)} + \pi$$
/ /3*pi\\
|sin|----|| / _________________________\
| \ 16 /| | / 2/3*pi\ 2/5*pi\ |
x12 = - atan|---------| - I*log| / sin |----| + sin |----| |
| /5*pi\| \\/ \ 16 / \ 16 / /
|sin|----||
\ \ 16 //
$$x_{12} = - \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{5 \pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \sin^{2}{\left(\frac{5 \pi}{16} \right)}} \right)}$$
x12 = -atan(sin(3*pi/16)/sin(5*pi/16)) - i*log(sqrt(sin(3*pi/16)^2 + sin(5*pi/16)^2))
Suma y producto de raíces
[src]
suma
/ /pi\\ / /pi\\ / /3*pi\\ / /5*pi\\ / /3*pi\\ / /3*pi\\
|cos|--|| / _____________________\ |cos|--|| / _____________________\ / _________________________\ |cos|----|| / _________________________\ |sin|----|| |sin|----|| / _________________________\ |sin|----|| / _________________________\
7*pi 3*pi pi pi 5*pi / 16____\ | \16/| | / 2/pi\ 2/pi\ | | \16/| | / 2/pi\ 2/pi\ | | / 2/3*pi\ 2/3*pi\ | | \ 16 /| | / 2/3*pi\ 2/5*pi\ | | \ 16 /| | \ 16 /| | / 2/3*pi\ 2/5*pi\ | | \ 16 /| | / 2/3*pi\ 2/5*pi\ |
- ---- - ---- + -- + -- + ---- - I*log\-\/ -1 / + pi - atan|-------| - I*log| / cos |--| + sin |--| | + - atan|-------| - I*log| / cos |--| + sin |--| | + -pi - I*log| / cos |----| + sin |----| | + atan|---------| + - I*log| / sin |----| + sin |----| | + atan|---------| + pi - atan|---------| - I*log| / sin |----| + sin |----| | + - atan|---------| - I*log| / sin |----| + sin |----| |
8 8 16 8 8 | /pi\| \\/ \16/ \16/ / | /pi\| \\/ \16/ \16/ / \\/ \ 16 / \ 16 / / | /3*pi\| \\/ \ 16 / \ 16 / / | /3*pi\| | /5*pi\| \\/ \ 16 / \ 16 / / | /5*pi\| \\/ \ 16 / \ 16 / /
|sin|--|| |sin|--|| |sin|----|| |sin|----|| |sin|----|| |sin|----||
\ \16// \ \16// \ \ 16 // \ \ 16 // \ \ 16 // \ \ 16 //
$$\left(- \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{5 \pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \sin^{2}{\left(\frac{5 \pi}{16} \right)}} \right)}\right) + \left(\left(\left(\left(\left(\left(- i \log{\left(- \sqrt[16]{-1} \right)} + \left(\left(\left(\left(- \frac{7 \pi}{8} - \frac{3 \pi}{8}\right) + \frac{\pi}{16}\right) + \frac{\pi}{8}\right) + \frac{5 \pi}{8}\right)\right) + \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{16} \right)}}{\sin{\left(\frac{\pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{16} \right)} + \cos^{2}{\left(\frac{\pi}{16} \right)}} \right)} + \pi\right)\right) + \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{16} \right)}}{\sin{\left(\frac{\pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{16} \right)} + \cos^{2}{\left(\frac{\pi}{16} \right)}} \right)}\right)\right) + \left(- \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \cos^{2}{\left(\frac{3 \pi}{16} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{3 \pi}{16} \right)}} \right)}\right)\right) + \left(- i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \sin^{2}{\left(\frac{5 \pi}{16} \right)}} \right)} + \operatorname{atan}{\left(\frac{\sin{\left(\frac{5 \pi}{16} \right)}}{\sin{\left(\frac{3 \pi}{16} \right)}} \right)}\right)\right) + \left(- \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{5 \pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \sin^{2}{\left(\frac{5 \pi}{16} \right)}} \right)} + \pi\right)\right)$$
=
/ /pi\\ / /3*pi\\ / /3*pi\\ / /5*pi\\
|cos|--|| |sin|----|| / _________________________\ / _________________________\ / _____________________\ |cos|----|| |sin|----||
| \16/| | \ 16 /| 9*pi | / 2/3*pi\ 2/3*pi\ | / 16____\ | / 2/3*pi\ 2/5*pi\ | | / 2/pi\ 2/pi\ | | \ 16 /| | \ 16 /|
- 2*atan|-------| - 2*atan|---------| + ---- - I*log| / cos |----| + sin |----| | - I*log\-\/ -1 / - 3*I*log| / sin |----| + sin |----| | - 2*I*log| / cos |--| + sin |--| | + atan|---------| + atan|---------|
| /pi\| | /5*pi\| 16 \\/ \ 16 / \ 16 / / \\/ \ 16 / \ 16 / / \\/ \16/ \16/ / | /3*pi\| | /3*pi\|
|sin|--|| |sin|----|| |sin|----|| |sin|----||
\ \16// \ \ 16 // \ \ 16 // \ \ 16 //
$$- i \log{\left(- \sqrt[16]{-1} \right)} - 2 \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{16} \right)}}{\sin{\left(\frac{\pi}{16} \right)}} \right)} - 2 \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{5 \pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \cos^{2}{\left(\frac{3 \pi}{16} \right)}} \right)} - 3 i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \sin^{2}{\left(\frac{5 \pi}{16} \right)}} \right)} - 2 i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{16} \right)} + \cos^{2}{\left(\frac{\pi}{16} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{3 \pi}{16} \right)}} \right)} + \operatorname{atan}{\left(\frac{\sin{\left(\frac{5 \pi}{16} \right)}}{\sin{\left(\frac{3 \pi}{16} \right)}} \right)} + \frac{9 \pi}{16}$$
producto
/ / /pi\\ \ / / /pi\\ \ / / /3*pi\\\ / / /5*pi\\\ / / /3*pi\\ \ / / /3*pi\\ \
| |cos|--|| / _____________________\| | |cos|--|| / _____________________\| | / _________________________\ |cos|----||| | / _________________________\ |sin|----||| | |sin|----|| / _________________________\| | |sin|----|| / _________________________\|
-7*pi -3*pi pi pi 5*pi / / 16____\\ | | \16/| | / 2/pi\ 2/pi\ || | | \16/| | / 2/pi\ 2/pi\ || | | / 2/3*pi\ 2/3*pi\ | | \ 16 /|| | | / 2/3*pi\ 2/5*pi\ | | \ 16 /|| | | \ 16 /| | / 2/3*pi\ 2/5*pi\ || | | \ 16 /| | / 2/3*pi\ 2/5*pi\ ||
-----*-----*--*--*----*\-I*log\-\/ -1 //*|pi - atan|-------| - I*log| / cos |--| + sin |--| ||*|- atan|-------| - I*log| / cos |--| + sin |--| ||*|-pi - I*log| / cos |----| + sin |----| | + atan|---------||*|- I*log| / sin |----| + sin |----| | + atan|---------||*|pi - atan|---------| - I*log| / sin |----| + sin |----| ||*|- atan|---------| - I*log| / sin |----| + sin |----| ||
8 8 16 8 8 | | /pi\| \\/ \16/ \16/ /| | | /pi\| \\/ \16/ \16/ /| | \\/ \ 16 / \ 16 / / | /3*pi\|| | \\/ \ 16 / \ 16 / / | /3*pi\|| | | /5*pi\| \\/ \ 16 / \ 16 / /| | | /5*pi\| \\/ \ 16 / \ 16 / /|
| |sin|--|| | | |sin|--|| | | |sin|----||| | |sin|----||| | |sin|----|| | | |sin|----|| |
\ \ \16// / \ \ \16// / \ \ \ 16 /// \ \ \ 16 /// \ \ \ 16 // / \ \ \ 16 // /
$$- i \log{\left(- \sqrt[16]{-1} \right)} \frac{5 \pi}{8} \frac{\pi}{8} \frac{\pi}{16} \cdot - \frac{7 \pi}{8} \left(- \frac{3 \pi}{8}\right) \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{16} \right)}}{\sin{\left(\frac{\pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{16} \right)} + \cos^{2}{\left(\frac{\pi}{16} \right)}} \right)} + \pi\right) \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{16} \right)}}{\sin{\left(\frac{\pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{16} \right)} + \cos^{2}{\left(\frac{\pi}{16} \right)}} \right)}\right) \left(- \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \cos^{2}{\left(\frac{3 \pi}{16} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{3 \pi}{16} \right)}} \right)}\right) \left(- i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \sin^{2}{\left(\frac{5 \pi}{16} \right)}} \right)} + \operatorname{atan}{\left(\frac{\sin{\left(\frac{5 \pi}{16} \right)}}{\sin{\left(\frac{3 \pi}{16} \right)}} \right)}\right) \left(- \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{5 \pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \sin^{2}{\left(\frac{5 \pi}{16} \right)}} \right)} + \pi\right) \left(- \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{5 \pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \sin^{2}{\left(\frac{5 \pi}{16} \right)}} \right)}\right)$$
=
/ / ___________ \\ / / ___________ \\ / / ___________\\ / ___________ \ / ___________ \ / ___________\
| | / ___ || | | / ___ || | | / ___ || | / ___ | | / ___ | | / ___ |
5 | | \/ 2 + \/ 2 || | | \/ 2 - \/ 2 || | |2 - \/ 2 - \/ 2 || | \/ 2 - \/ 2 | | \/ 2 + \/ 2 | |2 - \/ 2 - \/ 2 | / 16____\
105*I*pi *|pi + atan|-------------------||*|-pi - atan|-------------------||*|-pi + atan|------------------||*atan|-------------------|*atan|-------------------|*atan|------------------|*log\-\/ -1 /
| | ___________|| | | ___________|| | | ___________ || | ___________| | ___________| | ___________ |
| | / ___ || | | / ___ || | | / ___ || | / ___ | | / ___ | | / ___ |
\ \-2 + \/ 2 - \/ 2 // \ \-2 + \/ 2 + \/ 2 // \ \ \/ 2 + \/ 2 // \-2 + \/ 2 + \/ 2 / \-2 + \/ 2 - \/ 2 / \ \/ 2 + \/ 2 /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
65536
$$\frac{105 i \pi^{5} \left(- \pi - \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{-2 + \sqrt{\sqrt{2} + 2}} \right)}\right) \left(- \pi + \operatorname{atan}{\left(\frac{2 - \sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)}\right) \left(\operatorname{atan}{\left(\frac{\sqrt{\sqrt{2} + 2}}{-2 + \sqrt{2 - \sqrt{2}}} \right)} + \pi\right) \log{\left(- \sqrt[16]{-1} \right)} \operatorname{atan}{\left(\frac{\sqrt{\sqrt{2} + 2}}{-2 + \sqrt{2 - \sqrt{2}}} \right)} \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{-2 + \sqrt{\sqrt{2} + 2}} \right)} \operatorname{atan}{\left(\frac{2 - \sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)}}{65536}$$
105*i*pi^5*(pi + atan(sqrt(2 + sqrt(2))/(-2 + sqrt(2 - sqrt(2)))))*(-pi - atan(sqrt(2 - sqrt(2))/(-2 + sqrt(2 + sqrt(2)))))*(-pi + atan((2 - sqrt(2 - sqrt(2)))/sqrt(2 + sqrt(2))))*atan(sqrt(2 - sqrt(2))/(-2 + sqrt(2 + sqrt(2))))*atan(sqrt(2 + sqrt(2))/(-2 + sqrt(2 - sqrt(2))))*atan((2 - sqrt(2 - sqrt(2)))/sqrt(2 + sqrt(2)))*log(-(-1)^(1/16))/65536
Respuesta numérica
[src]
x1 = 1.96349540849362
x2 = 6.67588438887831
x3 = 66.169795266235
x4 = 45.9457925587507
x5 = 92.0879346583508
x6 = -17.8678082172919
x7 = 40.2516558741192
x8 = 82.0741080750334
x9 = -10.0138265833175
x10 = 88.1609438413636
x11 = -93.8550805259951
x12 = -43.7859476094077
x13 = 70.0967860832223
x14 = 8.05033117482385
x15 = 23.9546439836222
x16 = -90.1244392498572
x17 = -3.73064127613788
x18 = 22.1874981159779
x19 = -15.3152641862502
x20 = 16.1006623496477
x21 = -7.65763209312512
x22 = -56.3523182237669
x23 = 80.3069622073891
x24 = -24.1509935244715
x25 = 62.2428044492478
x26 = -53.9961237335746
x27 = 41.233403578366
x28 = -73.6310778185108
x29 = -71.8639319508665
x30 = -91.6952355766521
x31 = -47.712938426395
x32 = 30.8268779133498
x33 = -55.5669200603695
x34 = -68.1332906747286
x35 = -2.15984494934298
x36 = 44.1786466911065
x37 = 89.9280897090078
x38 = -21.7947990342792
x39 = -42.0188017417635
x40 = -100.334615374024
x41 = 18.2605072989907
x42 = 36.324665057132
x43 = -13.7444678594553
x44 = -5.89048622548086
x45 = -39.8589567924205
x46 = 84.2339530243763
x47 = 52.2289778659303
x48 = 58.3158136322605
x49 = 60.0829594999048
x50 = -20.0276531666349
x51 = -87.7682447596649
x52 = -27.8816348006094
x53 = -25.7217898512664
x54 = 67.9369411338793
x55 = 33.9684705669396
x56 = 94.4441291485432
x57 = -49.872783375738
x58 = -57.7267650097125
x59 = -46.1421420996001
x60 = 72.4529805734146
x61 = 63.0282026126452
x62 = 96.0149254753381
x63 = 30.2378292908018
x64 = -79.717913584841
x65 = -65.7770961845363
x66 = 4.1233403578366
x67 = -61.8501053675491
x68 = 99.9419162923253
x69 = -32.004975158446
x70 = 7.2649330114264
x71 = 166.897109721958
x72 = 48.1056375080937
x73 = 85.2157007286231
x74 = -83.8412539426776
x75 = 26.1144889329652
x76 = 55.9596191420682
x77 = -10.6028752058656
x78 = -97.9784208838317
x79 = 0.196349540849362
x80 = 11.9773219918111
x81 = 38.0918109247762
x82 = -64.009950316892
x83 = -80.6996612890878
x84 = -78.3434667988955
x85 = -69.7040870015235
x86 = 28.6670329640069
x87 = 8.24668071567321
x88 = 77.9507677171967
x89 = 50.6581815391354
x90 = -86.0010988920206
x91 = -51.6399292433822
x92 = -35.7356164345839
x93 = -75.9872723087031
x94 = -95.6222263936393
x95 = -29.6487806682537
x96 = 14.3335164820034
x96 = 14.3335164820034