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Ecuación x+9=0
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Ecuación 3,4+2y=7(y-2,3)
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Ecuación 9x-4x+39=94
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- -16*x+3*y=17
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- 11*x-6*y=5
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Expresiones idénticas
- 3cos(3x)-5sin(3x)-3cos(x)+3sin(x)= cero
- 3 coseno de (3x) menos 5 seno de (3x) menos 3 coseno de (x) más 3 seno de (x) es igual a 0
- 3 coseno de (3x) menos 5 seno de (3x) menos 3 coseno de (x) más 3 seno de (x) es igual a cero
- 3cos3x-5sin3x-3cosx+3sinx=0
- 3cos(3x)-5sin(3x)-3cos(x)+3sin(x)=O
-
Expresiones semejantes
- 3cos(3x)-5sin(3x)+3cos(x)+3sin(x)=0
- 3cos(3x)+5sin(3x)-3cos(x)+3sin(x)=0
- 3cos(3x)-5sin(3x)-3cos(x)-3sin(x)=0
- 3cos(3x)-5sin(3x)-3cosx+3sinx=0
3cos(3x)-5sin(3x)-3cos(x)+3sin(x)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3*cos(3*x) - 5*sin(3*x) - 3*cos(x) + 3*sin(x) = 0
$$\left(\left(- 5 \sin{\left(3 x \right)} + 3 \cos{\left(3 x \right)}\right) - 3 \cos{\left(x \right)}\right) + 3 \sin{\left(x \right)} = 0$$
Suma y producto de raíces
[src]
suma
/ / / ____\\\ / / / ____\\\
| | |-3 + 5*\/ 33 ||| | | |-3 - 5*\/ 33 |||
| |atan|-------------||| | |atan|-------------|||
| | | ____||| | | | ____|||
| | \-5 - 3*\/ 33 /|| | | \-5 + 3*\/ 33 /||
/ / ____ ____\ \ / / ____ ____\ \ |cos|-------------------|| |sin|-------------------||
I*\- log\-5 - 3*I + 3*\/ 33 - 5*I*\/ 33 / + log(34)/ I*\- log\-5 - 3*I - 3*\/ 33 + 5*I*\/ 33 / + log(34)/ | \ 2 /| /log(34) / ____\\ /log(34) / ____\\ | \ 2 /|
pi + ----------------------------------------------------- + ----------------------------------------------------- + -pi - atan|------------------------| + I*|------- - log\\/ 34 /| + pi + I*|------- - log\\/ 34 /| + atan|------------------------|
2 2 | / / ____\\| \ 2 / \ 2 / | / / ____\\|
| | |-3 + 5*\/ 33 ||| | | |-3 - 5*\/ 33 |||
| |atan|-------------||| | |atan|-------------|||
| | | ____||| | | | ____|||
| | \-5 - 3*\/ 33 /|| | | \-5 + 3*\/ 33 /||
|sin|-------------------|| |cos|-------------------||
\ \ 2 // \ \ 2 //
$$\left(\operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{- 5 \sqrt{33} - 3}{-5 + 3 \sqrt{33}} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{- 5 \sqrt{33} - 3}{-5 + 3 \sqrt{33}} \right)}}{2} \right)}} \right)} + \pi + i \left(- \log{\left(\sqrt{34} \right)} + \frac{\log{\left(34 \right)}}{2}\right)\right) + \left(\left(- \pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{-3 + 5 \sqrt{33}}{- 3 \sqrt{33} - 5} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{-3 + 5 \sqrt{33}}{- 3 \sqrt{33} - 5} \right)}}{2} \right)}} \right)} + i \left(- \log{\left(\sqrt{34} \right)} + \frac{\log{\left(34 \right)}}{2}\right)\right) + \left(\frac{i \left(\log{\left(34 \right)} - \log{\left(- 3 \sqrt{33} - 5 - 3 i + 5 \sqrt{33} i \right)}\right)}{2} + \left(\pi + \frac{i \left(\log{\left(34 \right)} - \log{\left(-5 + 3 \sqrt{33} - 5 \sqrt{33} i - 3 i \right)}\right)}{2}\right)\right)\right)$$
=
/ / / ____\\\ / / / ____\\\
| | |-3 + 5*\/ 33 ||| | | |-3 - 5*\/ 33 |||
| |atan|-------------||| | |atan|-------------|||
| | | ____||| | | | ____|||
| | \-5 - 3*\/ 33 /|| | | \-5 + 3*\/ 33 /||
|cos|-------------------|| / / ____ ____\ \ / / ____ ____\ \ |sin|-------------------||
| \ 2 /| I*\- log\-5 - 3*I - 3*\/ 33 + 5*I*\/ 33 / + log(34)/ I*\- log\-5 - 3*I + 3*\/ 33 - 5*I*\/ 33 / + log(34)/ /log(34) / ____\\ | \ 2 /|
pi - atan|------------------------| + ----------------------------------------------------- + ----------------------------------------------------- + 2*I*|------- - log\\/ 34 /| + atan|------------------------|
| / / ____\\| 2 2 \ 2 / | / / ____\\|
| | |-3 + 5*\/ 33 ||| | | |-3 - 5*\/ 33 |||
| |atan|-------------||| | |atan|-------------|||
| | | ____||| | | | ____|||
| | \-5 - 3*\/ 33 /|| | | \-5 + 3*\/ 33 /||
|sin|-------------------|| |cos|-------------------||
\ \ 2 // \ \ 2 //
$$\operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{- 5 \sqrt{33} - 3}{-5 + 3 \sqrt{33}} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{- 5 \sqrt{33} - 3}{-5 + 3 \sqrt{33}} \right)}}{2} \right)}} \right)} - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{-3 + 5 \sqrt{33}}{- 3 \sqrt{33} - 5} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{-3 + 5 \sqrt{33}}{- 3 \sqrt{33} - 5} \right)}}{2} \right)}} \right)} + \pi + \frac{i \left(\log{\left(34 \right)} - \log{\left(-5 + 3 \sqrt{33} - 5 \sqrt{33} i - 3 i \right)}\right)}{2} + \frac{i \left(\log{\left(34 \right)} - \log{\left(- 3 \sqrt{33} - 5 - 3 i + 5 \sqrt{33} i \right)}\right)}{2} + 2 i \left(- \log{\left(\sqrt{34} \right)} + \frac{\log{\left(34 \right)}}{2}\right)$$
producto
/ / / / ____\\\ \ / / / / ____\\\\
| | | |-3 + 5*\/ 33 ||| | | | | |-3 - 5*\/ 33 ||||
| | |atan|-------------||| | | | |atan|-------------||||
| | | | ____||| | | | | | ____||||
| | | \-5 - 3*\/ 33 /|| | | | | \-5 + 3*\/ 33 /|||
/ / ____ ____\ \ / / ____ ____\ \ | |cos|-------------------|| | | |sin|-------------------|||
I*\- log\-5 - 3*I + 3*\/ 33 - 5*I*\/ 33 / + log(34)/ I*\- log\-5 - 3*I - 3*\/ 33 + 5*I*\/ 33 / + log(34)/ | | \ 2 /| /log(34) / ____\\| | /log(34) / ____\\ | \ 2 /||
0*pi*-----------------------------------------------------*-----------------------------------------------------*|-pi - atan|------------------------| + I*|------- - log\\/ 34 /||*|pi + I*|------- - log\\/ 34 /| + atan|------------------------||
2 2 | | / / ____\\| \ 2 /| | \ 2 / | / / ____\\||
| | | |-3 + 5*\/ 33 ||| | | | | |-3 - 5*\/ 33 ||||
| | |atan|-------------||| | | | |atan|-------------||||
| | | | ____||| | | | | | ____||||
| | | \-5 - 3*\/ 33 /|| | | | | \-5 + 3*\/ 33 /|||
| |sin|-------------------|| | | |cos|-------------------|||
\ \ \ 2 // / \ \ \ 2 ///
$$\frac{i \left(\log{\left(34 \right)} - \log{\left(- 3 \sqrt{33} - 5 - 3 i + 5 \sqrt{33} i \right)}\right)}{2} \cdot 0 \pi \frac{i \left(\log{\left(34 \right)} - \log{\left(-5 + 3 \sqrt{33} - 5 \sqrt{33} i - 3 i \right)}\right)}{2} \left(- \pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{-3 + 5 \sqrt{33}}{- 3 \sqrt{33} - 5} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{-3 + 5 \sqrt{33}}{- 3 \sqrt{33} - 5} \right)}}{2} \right)}} \right)} + i \left(- \log{\left(\sqrt{34} \right)} + \frac{\log{\left(34 \right)}}{2}\right)\right) \left(\operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{- 5 \sqrt{33} - 3}{-5 + 3 \sqrt{33}} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{- 5 \sqrt{33} - 3}{-5 + 3 \sqrt{33}} \right)}}{2} \right)}} \right)} + \pi + i \left(- \log{\left(\sqrt{34} \right)} + \frac{\log{\left(34 \right)}}{2}\right)\right)$$
=
0
$$0$$
0
Respuesta rápida
[src]
x1 = 0
$$x_{1} = 0$$
x2 = pi
$$x_{2} = \pi$$
/ / ____ ____\ \
I*\- log\-5 - 3*I + 3*\/ 33 - 5*I*\/ 33 / + log(34)/
x3 = -----------------------------------------------------
2
$$x_{3} = \frac{i \left(\log{\left(34 \right)} - \log{\left(-5 + 3 \sqrt{33} - 5 \sqrt{33} i - 3 i \right)}\right)}{2}$$
/ / ____ ____\ \
I*\- log\-5 - 3*I - 3*\/ 33 + 5*I*\/ 33 / + log(34)/
x4 = -----------------------------------------------------
2
$$x_{4} = \frac{i \left(\log{\left(34 \right)} - \log{\left(- 3 \sqrt{33} - 5 - 3 i + 5 \sqrt{33} i \right)}\right)}{2}$$
/ / / ____\\\
| | |-3 + 5*\/ 33 |||
| |atan|-------------|||
| | | ____|||
| | \-5 - 3*\/ 33 /||
|cos|-------------------||
| \ 2 /| /log(34) / ____\\
x5 = -pi - atan|------------------------| + I*|------- - log\\/ 34 /|
| / / ____\\| \ 2 /
| | |-3 + 5*\/ 33 |||
| |atan|-------------|||
| | | ____|||
| | \-5 - 3*\/ 33 /||
|sin|-------------------||
\ \ 2 //
$$x_{5} = - \pi - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{-3 + 5 \sqrt{33}}{- 3 \sqrt{33} - 5} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{-3 + 5 \sqrt{33}}{- 3 \sqrt{33} - 5} \right)}}{2} \right)}} \right)} + i \left(- \log{\left(\sqrt{34} \right)} + \frac{\log{\left(34 \right)}}{2}\right)$$
/ / / ____\\\
| | |-3 - 5*\/ 33 |||
| |atan|-------------|||
| | | ____|||
| | \-5 + 3*\/ 33 /||
|sin|-------------------||
/log(34) / ____\\ | \ 2 /|
x6 = pi + I*|------- - log\\/ 34 /| + atan|------------------------|
\ 2 / | / / ____\\|
| | |-3 - 5*\/ 33 |||
| |atan|-------------|||
| | | ____|||
| | \-5 + 3*\/ 33 /||
|cos|-------------------||
\ \ 2 //
$$x_{6} = \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{- 5 \sqrt{33} - 3}{-5 + 3 \sqrt{33}} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(\frac{- 5 \sqrt{33} - 3}{-5 + 3 \sqrt{33}} \right)}}{2} \right)}} \right)} + \pi + i \left(- \log{\left(\sqrt{34} \right)} + \frac{\log{\left(34 \right)}}{2}\right)$$
x6 = atan(sin(atan((-5*sqrt(33) - 3)/(-5 + 3*sqrt(33)))/2)/cos(atan((-5*sqrt(33) - 3)/(-5 + 3*sqrt(33)))/2)) + pi + i*(-log(sqrt(34)) + log(34)/2)
Respuesta numérica
[src]
x1 = 68.5136746707636
x2 = -91.7075506623158
x3 = 81.6814089933346
x4 = 32.5577097443803
x5 = 29.4161170907905
x6 = -17.7077727130564
x7 = 59.6902604182061
x8 = -61.6900698633135
x9 = 41.9824877051497
x10 = -75.9995873943669
x11 = -21.9911485751286
x12 = 15.707963267949
x13 = -52.2652919025441
x14 = -19.4509196297506
x15 = -81.6814089933346
x16 = 70.2568215874578
x17 = 98.531155469766
x18 = 31.4159265358979
x19 = 40.2393407884555
x20 = -94.2477796076938
x21 = -67.973255170493
x22 = -3.74295636180161
x23 = -39.6989212881849
x24 = -59.6902604182061
x25 = -43.9822971502571
x26 = 26.2745244372007
x27 = 43.9822971502571
x28 = 79.6815995482272
x29 = 85.9647848554068
x30 = -15.707963267949
x31 = -45.9821065953645
x32 = 46.5225260956351
x33 = 11.9650069061474
x34 = -97.9907359694954
x35 = -74.2564404776726
x36 = 0.0
x37 = -65.9734457253857
x38 = 77.938452631533
x39 = 48.2656730123293
x40 = -28.2743338823081
x41 = 13.7081538228416
x42 = -10.0261416689812
x43 = -63.4332167800077
x44 = -50.2654824574367
x45 = 103.071193860251
x46 = -30.2741433274155
x47 = 18.2481922133269
x48 = -23.9909580202359
x49 = 84.2216379387126
x50 = 54.5488583195089
x51 = 28.2743338823081
x52 = 65.9734457253857
x53 = 33.9561554812759
x54 = -8.28299475228698
x55 = -32.0172902441098
x56 = -25.7341049369302
x57 = 4.2833758620722
x58 = 19.9913391300212
x59 = -87.9645943005142
x60 = -6.28318530717959
x61 = -1.99980944510739
x62 = 2.54022894537798
x63 = 57.6904509730987
x64 = -85.4243653551362
x65 = -47.7252535120587
x66 = 94.2477796076938
x67 = 92.2479701625864
x68 = 72.2566310325652
x69 = 24.5313775205065
x70 = 227.336454266948
x71 = 10.5665611692518
x72 = 99.9296012066616
x73 = -83.681218438442
x74 = 63.9736362802783
x75 = -9.42477796076938
x76 = 35.6993023979701
x77 = 62.230489363584
x78 = 90.5048232458922
x79 = -96.2475890528012
x80 = -69.7164020871873
x81 = 6.28318530717959
x82 = -53.4070751110265
x83 = 21.9911485751286
x84 = -54.0084388192383
x85 = 87.9645943005142
x86 = -72.2566310325652
x87 = 37.6991118430775
x88 = 50.2654824574367
x89 = 76.5400068946374
x90 = -37.6991118430775
x91 = 55.9473040564045
x92 = -89.9644037456216
x93 = -41.4420682048791
x93 = -41.4420682048791